11th Business Maths Weekly Test - 4 ( Matrices and Determinants )

MABS Institution

11th Business Maths Weekly Test - 4 ( Matrices and Determinants )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

If A=\(\begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix}\)and B=\(\begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}\)then, verify that (AB)^-1=B^-1A^-1

Show that \(\begin{vmatrix}x+a &b&c \\a &x+b&c\\a&b&x+c \end{vmatrix}=x^2(x+a+b+c)\)

Find the numbers a and b such that A²+aA+bI=0 for the matrix A=\(\begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}\)

Find the inverse of \(\begin{bmatrix}-1 & 5 \\-3 & 2 \end{bmatrix}.\)

Find the adjoint of the matrix \(\left[ \begin{matrix} 2 & -1 & 3 \\ 0 & 5 & 1 \\ 3 & 6 & 8 \end{matrix} \right] \)

Using the properties of determinants, show that \(\left| \begin{matrix} 2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86 \end{matrix} \right| \)=0

Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

Show that \(\begin{vmatrix} a & a+b&a+b+c \\2a &3a+2b &4a+3b+2c\\3a&6a+3b&10a+6b+3c \end{vmatrix}=a^3.\)

If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A²-4A+5I₂ = 0 and also find A^-1.

The technology matrix of an economic system of two industries is \(\left[ \begin{matrix} 0.8 & 0.2 \\ 0.9 & 0.7 \end{matrix} \right] \) Test whether the system is viable as per Hawkins – Simon conditions.

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11th Business Maths Weekly Test - 4 ( Matrices and Determinants )

MABS Institution

11th Business Maths Weekly Test - 4 ( Matrices and Determinants )-Aug 2020

Part - A

Generic 3 - Answer All Question

If A=\(\begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix}\)and B=\(\begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}\)then, verify that (AB)-1=B-1A-1

Show that \(\begin{vmatrix}x+a &b&c \\a &x+b&c\\a&b&x+c \end{vmatrix}=x^2(x+a+b+c)\)

Find the numbers a and b such that A2+aA+bI=0 for the matrix A=\(\begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}\)

Find the inverse of \(\begin{bmatrix}-1 & 5 \\-3 & 2 \end{bmatrix}.\)

Find the adjoint of the matrix \(\left[ \begin{matrix} 2 & -1 & 3 \\ 0 & 5 & 1 \\ 3 & 6 & 8 \end{matrix} \right] \)

Using the properties of determinants, show that \(\left| \begin{matrix} 2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86 \end{matrix} \right| \)=0

Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

Show that \(\begin{vmatrix} a & a+b&a+b+c \\2a &3a+2b &4a+3b+2c\\3a&6a+3b&10a+6b+3c \end{vmatrix}=a^3.\)

If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A2-4A+5I2 = 0 and also find A-1.

The technology matrix of an economic system of two industries is \(\left[ \begin{matrix} 0.8 & 0.2 \\ 0.9 & 0.7 \end{matrix} \right] \) Test whether the system is viable as per Hawkins – Simon conditions.

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Tamilnadu Stateboardszs - Class

If A=\(\begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix}\)and B=\(\begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}\)then, verify that (AB)^-1=B^-1A^-1

Find the numbers a and b such that A²+aA+bI=0 for the matrix A=\(\begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}\)

If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A²-4A+5I₂ = 0 and also find A^-1.