12th Business Maths Weekly Test - 4 ( Applications of Matrices and Determinants )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 4 ( Applications of Matrices and Determinants )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

if \(\left| A \right| \neq 0,\) then A is

non- singular matrix
singular matrix
zero matrix
none of these

Rank of a null matrix is

0
-1
\(\infty \)
1

if \(\rho (A)=\rho (A,B)\) then the system is

Consistent and has infinitely many solutions
Consistent and has a unique solution
Consistent
inconsistent

The rank of m×n matrix whose elements are unity is

if T=\(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right) \) is a transition probability matrix, then at equilibrium A is equal to

\(\frac { 1 }{ 4 } \)
\(\frac { 1 }{ 5 } \)
\(\frac { 1 }{ 6 } \)
\(\frac { 1 }{ 8 } \)

if \(\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },{ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix};\quad { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}\) then (x,y) is

\(\left( \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } \frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } } \right) \)
\(\left( \frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } } \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } \right) \)
\(\left( \frac { { \triangle }_{ 1 } }{ { \triangle }_{ 2 } } \frac { { \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right) \)
\(\left( \frac { { -\triangle }_{ 1 } }{ { \triangle }_{ 2 } } \frac { {- \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right) \)

If \(\rho (A)\) =r then which of the following is correct?

all the minors of order r which does not vanish
A has at least one minor of order r which does not vanish
A has at least one (r+1) order minor which vanishes
all (r+1) and higher order minors should not vanish

In a transition probability matrix, all the entries are greater than or equal to

Cramer’s rule is applicable only to get an unique solution when

\({ \triangle }_{ z }\neq 0\)
\({ \triangle }_{ x }\neq 0\)
\({ \triangle }_\neq 0\)
\({ \triangle }_{ y }\neq 0\)

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

there is only one solution
there exists infinitely many solutions
there is no solution
None of these

If A= \(\begin{pmatrix} 2 & 0 \\ 0 & 8 \end{pmatrix}\),then \(\rho (A)\) is

If \(\rho (A)=\rho (A,B)\)= the number of unknowns, then the system is

Consistent and has infinitely many solutions
Consistent and has a unique solution
inconsistent
consistent

IfA =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AA^Tis

The rank of the matrix \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is

The rank of the unit matrix of order n is

n −1
n
n +1
n²

If the rank of the matrix \(\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right) \) is 2. Then \(\lambda \) is

1
2
3
only real number

The system of equations 4x+6y=5, 6x+9y=7 has

a unique solution
no solution
infinitely many solutions
none of these

Which of the following is not an elementary transformation?

\({ R }_{ i }\leftrightarrow { R }_{ j }\)
\({ R }_{ i }\rightarrow { 2R }_{ i }+{ 2c }_{ j }\)
\({ R }_{ i }\rightarrow { 2R }_{ i }-{ 4R }_{ i }\)
\({ C }_{ i }\rightarrow { C }_{ i }+{ 5C }_{ j }\)

The rank of the diagonal matrix\(\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right) \)

if T= \(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right) \) is a transition probability matrix, then the value of x is

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

4
0
-4
1

If A=(1 2 3), then the rank of AA^T is

If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

\(\rho (A)=\rho (A,B)>n\)
\(\rho (A)=\rho (A,B)
\(\rho (A)=\rho (A,B)=n\)
none of these

if \(\rho (A)\neq \rho (A,B),\) then the system is

Consistent and has infinitely many solutions
Consistent and has a unique solution
inconsistent
consistent

\(\left| { A }_{ n\times n } \right| \)=3 \(\left| adjA \right| \) =243 then the value n is

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12th Business Maths Weekly Test - 4 ( Applications of Matrices and Determinants )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 4 ( Applications of Matrices and Determinants )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

if \(\left| A \right| \neq 0,\) then A is

Rank of a null matrix is

if \(\rho (A)=\rho (A,B)\) then the system is

The rank of m×n matrix whose elements are unity is

if T=\(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right) \) is a transition probability matrix, then at equilibrium A is equal to

If \(\rho (A)\) =r then which of the following is correct?

In a transition probability matrix, all the entries are greater than or equal to

Cramer’s rule is applicable only to get an unique solution when

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

If A= \(\begin{pmatrix} 2 & 0 \\ 0 & 8 \end{pmatrix}\),then \(\rho (A)\) is

If \(\rho (A)=\rho (A,B)\)= the number of unknowns, then the system is

IfA =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AAT is

The rank of the matrix \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is

The rank of the unit matrix of order n is

If the rank of the matrix \(\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right) \) is 2. Then \(\lambda \) is

The system of equations 4x+6y=5, 6x+9y=7 has

Which of the following is not an elementary transformation?

The rank of the diagonal matrix\(\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right) \)

if T= \(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right) \) is a transition probability matrix, then the value of x is

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

If A=(1 2 3), then the rank of AAT is

If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

if \(\rho (A)\neq \rho (A,B),\) then the system is

\(\left| { A }_{ n\times n } \right| \)=3 \(\left| adjA \right| \) =243 then the value n is

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IfA =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AA^Tis

If A=(1 2 3), then the rank of AA^T is