If A = begin{bmatrix} 1 & 2 & -1 3 & 0 & 2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given matrices $A = \begin{bmatrix} 1 & 2 & -1 \ 3 & 0 & 2 \ 4 & 5 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \ 2 & 1 & 0 \ 0 & 1 &

Vedclass · Accepted Answer

$\begin{bmatrix} 5 & 1 & -3 \ 3 & 2 & 6 \ 14 & 5 & 0 \end{bmatrix}$

Vedclass · Answer

(A) Given matrices $A = \begin{bmatrix} 1 & 2 & -1 \ 3 & 0 & 2 \ 4 & 5 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \ 2 & 1 & 0 \ 0 & 1 & 3 \end{bmatrix}$.To find $AB$,we perform matrix multiplication:$AB = \begin{bmatrix} (1)(1)+(2)(2)+(-1)(0) & (1)(0)+(2)(1)+(-1)(1) & (1)(0)+(2)(0)+(-1)(3) \ (3)(1)+(0)(2)+(2)(0) & (3)(0)+(0)(1)+(2)(1) & (3)(0)+(0)(0)+(2)(3) \ (4)(1)+(5)(2)+(0)(0) & (4)(0)+(5)(1)+(0)(1) & (4)(0)+(5)(0)+(0)(3) \end{bmatrix}$Calculating each element:Row $1$: $(1+4+0) = 5$,$(0+2-1) = 1$,$(0+0-3) = -3$Row $2$: $(3+0+0) = 3$,$(0+0+2) = 2$,$(0+0+6) = 6$Row $3$: $(4+10+0) = 14$,$(0+5+0) = 5$,$(0+0+0) = 0$Thus,$AB = \begin{bmatrix} 5 & 1 & -3 \ 3 & 2 & 6 \ 14 & 5 & 0 \end{bmatrix}$.

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

Similar Questions

If $A = \begin{bmatrix} i & 1 \\ 0 & i \end{bmatrix}$,then $A^4$ equals

If $A$ is a $3 \times 4$ matrix and $B$ is a matrix such that $A^{\prime}B$ and $BA^{\prime}$ are both defined,then $B$ is of the type:

If $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix}$,then:

If $A = \begin{bmatrix} 3 & \sqrt{3} & 2 \\ 4 & 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & -1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,verify that $(kB)^{\prime} = kB^{\prime}$,where $k$ is any constant.

The order of matrix $A$ is $m \times n$ and for matrix $B$,if $AB^{\prime}$ and $B^{\prime}A$ are defined,then the order of matrix $B$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module