Inverse of a Matrix

IMPORTANT

Inverse of a Matrix: Overview

This topic covers concepts, such as, Inverse of a Matrix Using Adjoint, Inverse of a Matrix, Matrix Polynomial Equation & Methods to Find Inverse of a Matrix etc.

Important Questions on Inverse of a Matrix

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IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 1

If $A = [\begin{matrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & - 1 & 0 \end{matrix}]$ then the value of $A^{2} - 3 A + 2 I$ would be:

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 2

The inverse of the following matrix using elementary operations would be:

$A = (\begin{matrix} 1 & 2 & - 2 \\ - 1 & 3 & 0 \\ 0 & - 2 & 1 \end{matrix})$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 3

If $A = [\begin{matrix} 3 & 2 \\ 1 & 1 \end{matrix}]$ , What would be the values of $a$ and $b$ such that $A^{2} + A a + b I = O$ ? Also find $A^{- 1}$ .

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 4

Using matrices, the solution of the following system of equations would be:

$\begin{array}{l} x + 2 y - 3 z = 6 \\ 3 x + 2 y - 2 z = 3 \\ 2 x - y + z = 2 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 5

If $A = [\begin{matrix} 6 & 5 \\ 7 & 6 \end{matrix}]$ would $A^{2} - 12 A + I = 0 ?$ Find value of $A^{- 1}$ also from the given options:

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 6

Using matrix method, the solution of the following system of linear equations would be :

$\begin{array}{l} x + y - z = 1 \\ x - y - z = - 1 \\ 3 x + y - 2 z = 3 \end{array}$

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 7

Using matrices, What would be the value of x,y,z for the given equations.

$\begin{array}{l} x + y - z = 3; 2 x + 3 y + z = 10; \\ 3 x - y - 7 z = 1 \end{array}$

HARD

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 8

Using matrices, What would be the value of $x, y, z$ for the given equations.

$\begin{array}{l} 3 x + 4 y + 7 z = 4 \\ 2 x - y + 3 z = - 3 \\ x + 2 y - 3 z = 8 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 9

Using matrices, The solution of the following system of equations would be

$2 x + 3 y + 3 z = 5, x - 2 y + z = - 4, 3 x - y - 2 z = 3$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 10

If $A = [\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}]$ then what would be the value of $A^{- 1}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 11

Using matrices, the solution of following system of equations would be:

$\begin{array}{l} 3 x - y + z = 5 \\ 2 x - 2 y + 3 z = 7 \\ x + y - z = - 1 \end{array}$

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 12

The matrix $X$ is such that $2 A + B + X = 0$ , where $A = [\begin{matrix} - 1 & 2 \\ 3 & 4 \end{matrix}]$ and $B = [\begin{matrix} 3 & - 2 \\ 1 & 5 \end{matrix}]$ . The matrix $X$ is:

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 13

$A = [\begin{matrix} 1 & 4 \\ 3 & 2 \end{matrix}]$ and $C = [\begin{matrix} a & b \\ c & d \end{matrix}]$ and $B$ is a matrix of order $2 \times 2$ . Prove the cancellation property of matrices and find matrix $B$ .

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 14

$A = [\begin{matrix} 1 & 5 \\ 3 & 3 \end{matrix}]$ and $C = [\begin{matrix} a & b \\ c & d \end{matrix}]$ and $B$ is a matrix of order $2 \times 2$ . Prove the cancellation property of matrices and find matrix $B$ .

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 15

$A = [\begin{matrix} 2 & 4 \\ 1 & 6 \end{matrix}]$ and $C = [\begin{matrix} a & b \\ c & d \end{matrix}]$ and $B$ is a matrix of order $2 \times 2$ . Prove the cancellation property of matrices and find matrix $B$ .

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 16

$A = [\begin{matrix} 1 & 3 \\ 4 & 5 \end{matrix}]$ and $C = [\begin{matrix} a & b \\ c & d \end{matrix}]$ and $B$ is a matrix of order $2 \times 2$ . Prove the cancellation property of matrices and find matrix $B$ .

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IMPORTANT

Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 17

$A = [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}]$ and $C = [\begin{matrix} a & b \\ c & d \end{matrix}]$ and $B$ is a matrix of order $2 \times 2$ . Prove the cancellation property of matrices and find matrix $B$ .

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 18

Given that $(\begin{matrix} 9 & 6 \\ 3 & 0 \end{matrix}) = (\begin{matrix} 2 & 3 \\ 1 & 0 \end{matrix}) (\begin{matrix} 3 & 0 \\ 1 & 2 \end{matrix})$ . Applying elementary row transformation $R_{1} \to R_{1} - 2 R_{2}$ on both sides, we get

MEDIUM

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 19

If $x \in R$ , then find the value of determinant $|\begin{array}{l} {(2^{x} + 2^{- x})}^{2} & {(2^{x} - 2^{- x})}^{2} & 1 \\ {(3^{x} + 3^{- x})}^{2} & {(3^{x} - 3^{- x})}^{2} & 1 \\ {(4^{x} + 4^{- x})}^{2} & {(4^{x} - 4^{- x})}^{2} & 1 \end{array}|$ .

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Mathematics>Matrices and Determinants>Inverse of a Matrix> Q 20

On using elementary column operations $C_{2} \to C_{2} - 2 C_{1}$ in the following matrix equation $[\begin{matrix} 1 & - 3 \\ 2 & 4 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 3 & 1 \\ 2 & 4 \end{matrix}]$ , we have

Inverse of a Matrix

Inverse of a Matrix: Overview

Important Questions on Inverse of a Matrix

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