11th Maths Weekly Test -3( Matrices and Determinants )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test -3( Matrices and Determinants )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

If A=\(\begin{bmatrix} 1 & -1 \\ 2 &-1 \end{bmatrix}\),B=\(\begin{bmatrix} a & 1 \\ b &-1 \end{bmatrix}\) and (A+B)²=A²+B², then the values of a and b are

a = 4, b =1
a =1, b = 4
a = 0, b = 4
a = 2, b = 4

Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?

A + B is a symmetric matrix
AB is a symmetric matrix
AB = (BA)^T
A^T B = AB^T

If \(\begin{bmatrix} 4 & 3 \\ -2 & x \end{bmatrix}\) is singular then the value of x is

\(\frac{3}{2}\)
-\(\frac{3}{2}\)
3
-2

|adj A| =_____________ where A is a square matrix of order

|A|
|A|²
|A|³
I

If A and B are square matrices of order 3 and |A|=5, |B|=3 then |3 AB| is

Which one of the following is not true about the matrix \(\begin{bmatrix} 1 &0 &0 \\ 0 & 0 &0 \\ 0 & 0 & 5 \end{bmatrix}?\)

a scalar matrix
a diagonal matrix
an upper triangular matrix
a lower triangular matrix

The negative of a matrix is obtained by multiplying it by

1
-1
I
A^T

If \(\triangle\)=\(\begin{vmatrix} a&b &c \\ x & y & z \\ p &q &r \end{vmatrix}\) ,then \(\begin{vmatrix} ka&kb &kc \\ kx & ky & kz \\k p &kq &kr \end{vmatrix}\)is

\(\triangle\)
k\(\triangle\)
3k\(\triangle\)
k³\(\triangle\)

If A=\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\) then A² is equal to

\(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\)
\(\begin{pmatrix} 1 & 0 \\ 1 & 0 \end{pmatrix}\)
\(\begin{pmatrix} 0 & 1 \\ 0 & 1 \end{pmatrix}\)
\(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)

On using elementary row operation R₁⟶R₁-3R₂ in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

Choose the incorrect statement

Matrix multiplication is non commutative
Matrix addition is associative
Singular matrices have inverse
Non singular matrices have inverse

The value of\(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+sin\theta & 1 \\ 1 & 1 & 1+cos\theta \end{matrix} \right| \) is

3
1
2
\(\frac{1}{2}\)

What must be the matrix X, if 2x+\(\begin{bmatrix} 1& 2 \\ 3 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}?\)

\(\begin{bmatrix} 1& 3 \\ 2 &-1 \end{bmatrix}\)
\(\begin{bmatrix} 1& -3 \\ 2 &-1 \end{bmatrix}\)
\(\begin{bmatrix} 2& 6 \\ 4 &-2 \end{bmatrix}\)
\(\begin{bmatrix} 2& -6 \\ 4 &-2 \end{bmatrix}\)

If A +I =\(\begin{bmatrix} 3& -2 \\ 4 & 1 \end{bmatrix},\) then (A+ I )(A-I ) is equal to

\(\begin{bmatrix} -5& -4 \\ 8 & -9 \end{bmatrix}\)
\(\begin{bmatrix} -5& 4 \\ -8 & 9 \end{bmatrix}\)
\(\begin{bmatrix} 5& 4 \\ 8 & 9 \end{bmatrix}\)
\(\begin{bmatrix} -5& -4 \\ -8 & -9 \end{bmatrix}\)

If A and B are two matrices such that A + B and AB are both defined, then

A and B are two matrices not necessarily of same order
A and B are square matrices of same order
Number of columns of A is equal to the number of rows of B
A = B.

If A(B+C)=AB + AC where A, B, C are matrices of the same order than the property applied is matrix multipication is

commutative
association
distributive over addition
distributive over multiplication

If A is a square matrix, then which of the following is not symmetric?

A+ A^T
AA^T
A^T A
A− A^T

If A is a matrix 3 x 3, then \({ { (A }^{ 2 }) }^{ -1 }\)=

\(\frac { 1 }{ { A }^{ 2 } } \)
A^-2
\({ { (A }^{ -1 }) }^{ 2 }\)
I

If A is skew-symmetric of order n and C is a column matrix of order n × 1, then C^T AC is

an identity matrix of order n
an identity matrix of order 1
a zero matrix of order 1
an identity matrix of order 2

If \(\begin{vmatrix}2a & x_1 &y_1 \\ 2b & x_2 & y_2 \\ 2c & x_3 &y_3 \end{vmatrix}={abc\over 2}\neq 0,\)then the area of the triangle whose vertices are \(\begin{pmatrix} {x_1\over a}, {y_1\over a} \end{pmatrix}\),\(\begin{pmatrix} {x_2\over b}, {y_2\over b} \end{pmatrix}\),\(\begin{pmatrix} {x_3\over c}, {y_3\over c} \end{pmatrix}\) is

\({1\over 4}\)
\({1\over 4} abc\)
\({1\over 8}\)
\({1\over 8}abc\)

A root of the equation \(\begin{vmatrix} 3-x&-6 &3 \\ -6 & 3-x & 3 \\ 3 &3 &-6-x \end{vmatrix}=0 \ is\)

6
3
0
-6

If A=\(\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}\) is a matrix satisfying the equation AA^T = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to

(2, - 1)
(- 2, 1)
(2, 1)
(- 2, - 1)

If \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\), then the value of x+y is

If a_ij=\({1\over2}(3i-2j)\) and A=[a_ij]_2x2 is

\(\begin{bmatrix} {1\over 2}& 2 \\ -{1\over2} & 1 \end{bmatrix}\)
\(\begin{bmatrix} {1\over 2}& -{1\over2} \\ 2& 1 \end{bmatrix}\)
\(\begin{bmatrix} 2& 2\\ {1\over 2}& -{1\over2} \end{bmatrix}\)
\(\begin{bmatrix} -{1\over 2}& {1\over2} \\ 1& 2 \end{bmatrix}\)

If f(x)=\(\left| \begin{matrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{matrix} \right| \) then

f(a)=0
f(b)=0
f(0)=0
f(1)=0

Assertion (A): The inverse of \(\\ \\ \\ \begin{bmatrix} 2 & -1 \\ -4 & 2 \end{bmatrix}\) does not exist.
Reason (R): The matrix is non-singular

Both A and R are true and R is the correct explanation of A
Both A and R are true and R is not a correct explantion of A
A is true but R is false
A is false but R is true

The matrix A satisfying the equation \(\begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}\)A=\(\begin{bmatrix} 1 & 1 \\ 0 & -1 \end{bmatrix}\)is

\(\begin{bmatrix} 1 & 4 \\ -1 & 0 \end{bmatrix}\)
\(\begin{bmatrix} 1 & -4 \\ 1 & 0 \end{bmatrix}\)
\(\begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}\)
\(\begin{bmatrix} 1 & -4 \\ 1 & 1 \end{bmatrix}\)

If A is a square matrix of order 3, then the number of minors in determinant of A are

If x₁,x₂,x₃ as well as y₁,y₂,y₃ are in geometric progression with the same common ratio, then the points (x₁, y₁ ), (x₂,y₂), (x₃,y₃ ) are

vertices of an equilateral triangle
vertices of a right angled triangle
vertices of a right angled isosceles triangle
collinear

If \(\left( \begin{matrix} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix} \right) \) is a singular matrix, then \(\lambda \) is

\(\lambda \)=2
\(\lambda \)≠2
\(\lambda =\frac { -8 }{ 5 } \)
\(\lambda \neq \frac { -8 }{ 5 } \)

If A and B are symmetric matrices of order n, where (A \(\neq\) B), then

A + B is skew-symmetric
A + B is symmetric
A + B is a diagonal matrix
A + B is a zero matrix

The value of \(\left| \begin{matrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{matrix} \right| \)=0, where a, b, c are in AP is

(x+1)(x+2)(x+3)
I
0
(x+a)(x+b)(x+c)

Find the odd one out of the following:

\(\begin{bmatrix} 0 & 2 \\ -2 & 0 \end{bmatrix}\)
\(\begin{bmatrix} 0 & \frac { -7 }{ 2 } \\ \frac { 7 }{ 2 } & 0 \end{bmatrix}\)
\(\begin{bmatrix} 0 & 3.2 \\ -3.2 & 0 \end{bmatrix}\)
\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\)

If the square of the matrix \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is the unit matrix of order 2, then\(\alpha ,\beta \) and \(\gamma\) should satisfy the relation.

1+\(\alpha ^2+\beta \gamma=0\)
1-\(\alpha ^2-\beta \gamma=0\)
1-\(\alpha ^2+\beta \gamma=0\)
1+\(\alpha ^2-\beta \gamma=0\)

If A= \(\begin{vmatrix}-1 & 2 &4 \\ 3 &1 &0 \\ -2& 4 &2 \end{vmatrix}\)and B=\(\begin{vmatrix}-2 & 4 &2 \\ 6 &2 &0 \\ -2& 4 &8 \end{vmatrix}\),then B is given by

B=4A
B=-4A
B=-A
B=6A

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11th Maths Weekly Test -3( Matrices and Determinants )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test -3( Matrices and Determinants )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

If A=\(\begin{bmatrix} 1 & -1 \\ 2 &-1 \end{bmatrix}\),B=\(\begin{bmatrix} a & 1 \\ b &-1 \end{bmatrix}\) and (A+B)2=A2+B2, then the values of a and b are

Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?

If \(\begin{bmatrix} 4 & 3 \\ -2 & x \end{bmatrix}\) is singular then the value of x is

|adj A| =_____________ where A is a square matrix of order

If A and B are square matrices of order 3 and |A|=5, |B|=3 then |3 AB| is

Which one of the following is not true about the matrix \(\begin{bmatrix} 1 &0 &0 \\ 0 & 0 &0 \\ 0 & 0 & 5 \end{bmatrix}?\)

The negative of a matrix is obtained by multiplying it by

If \(\triangle\)=\(\begin{vmatrix} a&b &c \\ x & y & z \\ p &q &r \end{vmatrix}\) ,then \(\begin{vmatrix} ka&kb &kc \\ kx & ky & kz \\k p &kq &kr \end{vmatrix}\)is

If A=\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\) then A2 is equal to

On using elementary row operation R1⟶R1-3R2 in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

Choose the incorrect statement

The value of\(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+sin\theta & 1 \\ 1 & 1 & 1+cos\theta \end{matrix} \right| \) is

What must be the matrix X, if 2x+\(\begin{bmatrix} 1& 2 \\ 3 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}?\)

If A +I =\(\begin{bmatrix} 3& -2 \\ 4 & 1 \end{bmatrix},\) then (A+ I )(A-I ) is equal to

If A and B are two matrices such that A + B and AB are both defined, then

If A(B+C)=AB + AC where A, B, C are matrices of the same order than the property applied is matrix multipication is

If A is a square matrix, then which of the following is not symmetric?

If A is a matrix 3 x 3, then \({ { (A }^{ 2 }) }^{ -1 }\)=

If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is

A root of the equation \(\begin{vmatrix} 3-x&-6 &3 \\ -6 & 3-x & 3 \\ 3 &3 &-6-x \end{vmatrix}=0 \ is\)

If A=\(\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}\) is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to

If \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\), then the value of x+y is

If aij =\({1\over2}(3i-2j)\) and A=[aij]2x2 is

If f(x)=\(\left| \begin{matrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{matrix} \right| \) then

Assertion (A): The inverse of \(\\ \\ \\ \begin{bmatrix} 2 & -1 \\ -4 & 2 \end{bmatrix}\) does not exist. Reason (R): The matrix is non-singular

The matrix A satisfying the equation \(\begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}\)A=\(\begin{bmatrix} 1 & 1 \\ 0 & -1 \end{bmatrix}\)is

If A is a square matrix of order 3, then the number of minors in determinant of A are

If x1,x2,x3 as well as y1,y2,y3 are in geometric progression with the same common ratio, then the points (x1, y1 ), (x2,y2), (x3,y3 ) are

If \(\left( \begin{matrix} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix} \right) \) is a singular matrix, then \(\lambda \) is

If A and B are symmetric matrices of order n, where (A \(\neq\) B), then

The value of \(\left| \begin{matrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{matrix} \right| \)=0, where a, b, c are in AP is

Find the odd one out of the following:

If the square of the matrix \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is the unit matrix of order 2, then\(\alpha ,\beta \) and \(\gamma\) should satisfy the relation.

If A= \(\begin{vmatrix}-1 & 2 &4 \\ 3 &1 &0 \\ -2& 4 &2 \end{vmatrix}\)and B=\(\begin{vmatrix}-2 & 4 &2 \\ 6 &2 &0 \\ -2& 4 &8 \end{vmatrix}\),then B is given by

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If A=\(\begin{bmatrix} 1 & -1 \\ 2 &-1 \end{bmatrix}\),B=\(\begin{bmatrix} a & 1 \\ b &-1 \end{bmatrix}\) and (A+B)²=A²+B², then the values of a and b are

If A=\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\) then A² is equal to

On using elementary row operation R₁⟶R₁-3R₂ in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

If A is skew-symmetric of order n and C is a column matrix of order n × 1, then C^T AC is

If A=\(\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}\) is a matrix satisfying the equation AA^T = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to

If a_ij=\({1\over2}(3i-2j)\) and A=[a_ij]_2x2 is

Assertion (A): The inverse of \(\\ \\ \\ \begin{bmatrix} 2 & -1 \\ -4 & 2 \end{bmatrix}\) does not exist.
Reason (R): The matrix is non-singular

If x₁,x₂,x₃ as well as y₁,y₂,y₃ are in geometric progression with the same common ratio, then the points (x₁, y₁ ), (x₂,y₂), (x₃,y₃ ) are