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Chapter 4: Q35. (page 200)

For Exercises 34-38, use the figure below.
35. Use matrix multiplication to find BA if $B = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}]$

Short Answer

Expert verified

The value ofBA is: $BA = [\begin{matrix} 0 & 8 & 4 & - 4 \\ 0 & 8 & 12 & 4 \end{matrix}]$

Step by step solution

01

- Observe the given figure.

The given figure is:

02

- Description of step.

It is being given that $B = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}]$

The vertex matrixA is given by: $A = [\begin{matrix} 0 & 4 & 2 & 鈭� 2 \\ 0 & 4 & 6 & 2 \end{matrix}]$

Therefore, the value of BA is given by: $\begin{matrix} B A = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] 鈰� [\begin{matrix} 0 & 4 & 2 & 鈭� 2 \\ 0 & 4 & 6 & 2 \end{matrix}] \\ = [\begin{matrix} 0 + 0 & 8 + 0 & 4 + 0 & 鈭� 4 + 0 \\ 0 + 0 & 0 + 8 & 0 + 12 & 0 + 4 \end{matrix}] \\ = [\begin{matrix} 0 & 8 & 4 & 鈭� 4 \\ 0 & 8 & 12 & 4 \end{matrix}] \end{matrix}$

03

- Write the value of BA.

The value of BA is: $B A = [\begin{matrix} 0 & 8 & 4 & 鈭� 4 \\ 0 & 8 & 12 & 4 \end{matrix}]$

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Most popular questions from this chapter

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.

For any matrix $A_{m 脳 n}$ for $m 鈮� n$ , $A^{2}$ is defined.

Perform the indicated matrix operation. If the matrix doesn鈥檛 exist, write impossible.

$[\begin{matrix} 1.35 & 5.80 \\ 1.24 & 14.32 \\ 6.10 & 35.26 \end{matrix}] + [\begin{matrix} 0.45 & 3.28 \\ 1.94 & 16.72 \\ 4.31 & 21.30 \end{matrix}]$

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ 鈭� 1 & 6 \\ 3 & 鈭� 9 \end{matrix}], 鈥夆赌� B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], 鈥夆赌� C = [\begin{matrix} 0 & 4 \\ 鈭� 2 & 5 \\ 7 & 鈭� 1 \end{matrix}], 鈥夆赌� D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ 鈭� 3 & 0 \end{matrix}]$

25. $D - B$

Solve each equation.

$[\begin{matrix} x^{2} + 1 & 5 - y \\ x + y & y - 4 \end{matrix}] = [\begin{matrix} 5 & x \\ 5 & 3 \end{matrix}]$

Determine whether each matrix product is defined. If so, state the dimensions of the product. $M_{4 脳 3} 鈰� N_{4 脳 3}$

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