Chapter 4: Q24. (page 164)

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.
$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$
24. $A + B$

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is $A + B = [\begin{matrix} 13 & 10 \\ 4 & 7 \\ 7 & - 5 \end{matrix}]$ .

Step by step solution

- Substitute the matrices

Substitute $[\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}]$ for A and $[\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}]$ for B into .

$A + B = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}] + [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}]$

- Perform the matrix addition

Matrix addition - If A and B are two matrices of order $m \times n$ , then the addition of the two matrices will also yield a matrix of order $m \times n$ wherein each element is the sum of the corresponding elements.

$\begin{matrix} A + B = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}] + [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}] \\ = [\begin{matrix} 5 + 8 & 7 + 3 \\ - 1 + 5 & 6 + 1 \\ 3 + 4 & - 9 + 4 \end{matrix}] \end{matrix}$

- Simplify

Further simplify the matrix.

$\begin{matrix} A + B = [\begin{matrix} 5 + 8 & 7 + 3 \\ - 1 + 5 & 6 + 1 \\ 3 + 4 & - 9 + 4 \end{matrix}] \\ = [\begin{matrix} 13 & 10 \\ 4 & 7 \\ 7 & - 5 \end{matrix}] \end{matrix}$

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Short Answer

Step by step solution

- Substitute the matrices

- Perform the matrix addition

- Simplify

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Use matricesA, B, Cand Dto find the following.A=57−163−9, B=835144, C=04−257−1, D=6290−3024. A+B

Short Answer

Step by step solution

- Substitute the matrices

- Perform the matrix addition

- Simplify

One App. One Place for Learning.

Most popular questions from this chapter

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