(C) Given $A = [1\, 2\, 3]$ (a $1 \times 3$ matrix) and $B = \begin{bmatrix} -5 & 4 & 0 \\ 0 & 2 & -1 \\ 1 & -3 & 2 \end{bmatrix}$ (a $3 \times 3$ mat

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$\begin{bmatrix} -2 & -1 & 4 \end{bmatrix}$

(C) Given $A = [1\, 2\, 3]$ (a $1 \times 3$ matrix) and $B = \begin{bmatrix} -5 & 4 & 0 \\ 0 & 2 & -1 \\ 1 & -3 & 2 \end{bmatrix}$ (a $3 \times 3$ matrix). To find $AB$,we multiply the row of $A$ by each column of $B$: $AB = [1 \times (-5) + 2 \times 0 + 3 \times 1, \quad 1 \times 4 + 2 \times 2 + 3 \times (-3), \quad 1 \times 0 + 2 \times (-1) + 3 \times 2]$ $AB = [-5 + 0 + 3, \quad 4 + 4 - 9, \quad 0 - 2 + 6]$ $AB = [-2, \quad -1, \quad 4]$ Thus,$AB = [-2\, -1\, 4]$.

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

Easy

If $A = [1\, 2\, 3]$ and $B = \begin{bmatrix} -5 & 4 & 0 \\ 0 & 2 & -1 \\ 1 & -3 & 2 \end{bmatrix}$,then $AB = $

A
$\begin{bmatrix} -5 & 4 & 0 \\ 0 & 4 & -2 \\ 3 & -9 & 6 \end{bmatrix}$
B
$\begin{bmatrix} 3 \\ 1 \\ 1 \end{bmatrix}$
C
$\begin{bmatrix} -2 & -1 & 4 \end{bmatrix}$
D
$\begin{bmatrix} -5 & 8 & 0 \\ 0 & 4 & -3 \\ 1 & -6 & 6 \end{bmatrix}$

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3 and 4 .Determinants and Matrices

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Types of matrices, Algebra of matrices

$A$ and $B$ are two given matrices such that the order of $A$ is $3 \times 4$. If $A'B$ and $BA'$ are both defined,then:

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If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ and $A^2 - 5A = kI$,then $k =$ . . . . . .

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Find the value of $x, y$ and $z$ from the following equation : $\begin{bmatrix} 4 & 3 \\ x & 5 \end{bmatrix} = \begin{bmatrix} y & z \\ 1 & 5 \end{bmatrix}$

Easy

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If $A = [1, 2, 3]$,$B = \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}$ and $C = \begin{bmatrix} 1 & 5 \\ 0 & 2 \end{bmatrix}$,then which of the following is defined?

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Let $A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$. Then the number of $3 \times 3$ matrices $B$ with entries from the set $\{1, 2, 3, 4, 5\}$ and satisfying $AB = BA$ is $....$

DifficultJEE MAIN 2021

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If $A = [1\, 2\, 3]$ and $B = \begin{bmatrix} -5 & 4 & 0 \\ 0 & 2 & -1 \\ 1 & -3 & 2 \end{bmatrix}$,then $AB = $

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$A$ and $B$ are two given matrices such that the order of $A$ is $3 \times 4$. If $A'B$ and $BA'$ are both defined,then:

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