(B) For the matrix multiplication $AB = C$ to be defined,the number of columns in matrix $A$ must be equal to the number of rows in matrix $B$. If $A$

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$A_{3 \times 2}, B_{2 \times 3}, C_{3 \times 3}$

(B) For the matrix multiplication $AB = C$ to be defined,the number of columns in matrix $A$ must be equal to the number of rows in matrix $B$. If $A$ is an $m \times n$ matrix and $B$ is an $n \times p$ matrix,then the resulting matrix $C$ will have the dimensions $m \times p$. Looking at option $B$: If $A$ is $3 \times 2$ and $B$ is $2 \times 3$,then $C$ must be a $3 \times 3$ matrix. Therefore,the correct dimensions are $A_{3 \times 2}, B_{2 \times 3}, C_{3 \times 3}$.

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

Easy

If $AB = C$,then the dimensions of matrices $A, B, C$ are:

A
$A_{2 \times 3}, B_{3 \times 2}, C_{2 \times 2}$
B
$A_{3 \times 2}, B_{2 \times 3}, C_{3 \times 3}$
C
$A_{3 \times 3}, B_{2 \times 3}, C_{3 \times 3}$
D
$A_{3 \times 2}, B_{2 \times 3}, C_{2 \times 2}$

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3-4. Matrices and Determinants

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Types of matrices, Algebra of matrices

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If $X_{4 \times 3}$, $Y_{4 \times 3}$ and $P_{2 \times 3}$ are matrices, then the order of the matrix $\left[P(X^T Y)^{-1} P^T\right]^T$ is

MediumTS EAMCET 2023

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If $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & -1 & 3 \\ -1 & 0 & 2 \end{bmatrix}$,then find $2A - B$.

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If $AB = C$,then the dimensions of matrices $A, B, C$ are:

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If $\begin{bmatrix} x & 0 \\ 1 & y \end{bmatrix} + \begin{bmatrix} -2 & 1 \\ 3 & 4 \end{bmatrix} = \begin{bmatrix} 3 & 5 \\ 6 & 3 \end{bmatrix} - \begin{bmatrix} 2 & 4 \\ 2 & 1 \end{bmatrix}$,then find the values of $x$ and $y$.

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