(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

An $n \times n$ matrix is formed using $0, 1$ and $-1$ as its elements. The number of such matrices which are skew-symmetric is

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Let $Q = \begin{bmatrix} \cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4} \end{bmatrix}$ and $x = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}$. Then $Q^{3} x$ is equal to:

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For a matrix $A$,the conditions $AI = A$ and $AA^T = I$ are true for:

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$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

EasyTS EAMCET 2001

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If $A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix}$ is such that $A^2 = I$, then . . . . . . .

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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

An $n \times n$ matrix is formed using $0, 1$ and $-1$ as its elements. The number of such matrices which are skew-symmetric is

Let $Q = \begin{bmatrix} \cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4} \end{bmatrix}$ and $x = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}$. Then $Q^{3} x$ is equal to:

For a matrix $A$,the conditions $AI = A$ and $AA^T = I$ are true for:

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

If $A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix}$ is such that $A^2 = I$, then . . . . . . .

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