(A) To add or subtract matrices,they must have the same order. Matrix $A$ is of order $3 \times 3$. Matrix $B$ is of order $3 \times 2$. In the expres

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(A) To add or subtract matrices,they must have the same order. Matrix $A$ is of order $3 \times 3$. Matrix $B$ is of order $3 \times 2$. In the expression $A^2 + 2B - 2A$,we are attempting to add matrix $A^2$ (which is $3 \times 3$) to matrix $2B$ (which is $3 \times 2$). Since the orders of $A^2$ and $2B$ are different,the addition is not defined. Therefore,the expression $A^2 + 2B - 2A$ is not defined.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Types of matrices, Algebra of matrices

Easy

If $A = \begin{bmatrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5 \end{bmatrix}$,$B = \begin{bmatrix} 2 & 4 \\ 0 & 1 \\ -1 & 2 \end{bmatrix}$,and $C = \begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix}$,then which of the following expressions is not defined?

A
$A^2 + 2B - 2A$
B
$CC'$
C
$B'C$
D
$AB$

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3 and 4 .Determinants and Matrices

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Types of matrices, Algebra of matrices

If $A = \begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix}$,then $A^n = 2^k A$,where $k = $

MediumKCET 2018

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If $A = \begin{bmatrix} 0 & 0 & -5 \\ 0 & -5 & 0 \\ -5 & 0 & 0 \end{bmatrix}$,then $A^2 =$ . . . . . . .

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If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{10} = $ . . . . . . .

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If $A = [a\, b]$,$B = [-b\, -a]$ and $C = \begin{bmatrix} a \\ -a \end{bmatrix}$,then the correct statement is

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Let $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$,$B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$,and $C = \begin{bmatrix} -2 & 5 \\ 3 & 4 \end{bmatrix}$. Find $A - B$.

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If $A = \begin{bmatrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5 \end{bmatrix}$,$B = \begin{bmatrix} 2 & 4 \\ 0 & 1 \\ -1 & 2 \end{bmatrix}$,and $C = \begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix}$,then which of the following expressions is not defined?

Similar Questions

If $A = \begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix}$,then $A^n = 2^k A$,where $k = $

If $A = \begin{bmatrix} 0 & 0 & -5 \\ 0 & -5 & 0 \\ -5 & 0 & 0 \end{bmatrix}$,then $A^2 =$ . . . . . . .

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Let $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$,$B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$,and $C = \begin{bmatrix} -2 & 5 \\ 3 & 4 \end{bmatrix}$. Find $A - B$.

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