Chapter 4: Q26. (page 164)

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

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is $4 C = [\begin{matrix} 0 & 16 \\ - 8 & 20 \\ 28 & - 4 \end{matrix}]$ .

Step by step solution

- Substitute the matrix

Substitute $[\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}]$ for C into $4 C$ .

$4 C = 4 [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}]$

- Perform the scalar multiplication

Scalar multiplication -The product of a scalar k and an $m \times n$ matrix is an $m \times n$ matrix in which each element equals k times the corresponding elements of the original matrix.

Multiply each element of the matrix $[\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}]$ by 4.

$\begin{matrix} 4 C = 4 [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}] \\ = [\begin{matrix} 4 (0) & 4 (4) \\ 4 (- 2) & 4 (5) \\ 4 (7) & 4 (- 1) \end{matrix}] \end{matrix}$

- Simplify

Further simplify the matrix.

$\begin{matrix} 4 C = [\begin{matrix} 4 (0) & 4 (4) \\ 4 (- 2) & 4 (5) \\ 4 (7) & 4 (- 1) \end{matrix}] \\ = [\begin{matrix} 0 & 16 \\ - 8 & 20 \\ 28 & - 4 \end{matrix}] \end{matrix}$

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Short Answer

Step by step solution

- Substitute the matrix

- Perform the scalar multiplication

- Simplify

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Use matrices A, B, Cand Dto find the following.A=57−163−9, B=835144, C=04−257−1, D=6290−304C

Short Answer

Step by step solution

- Substitute the matrix

- Perform the scalar multiplication

- Simplify

One App. One Place for Learning.

Most popular questions from this chapter

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