Q26. Use matrices A, B, C聽and D聽to ... [FREE SOLUTION]

Chapter 4: Q26. (page 164)

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

Short Answer

Expert verified

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

Step by step solution

- Substitute the matrix

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

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

- Perform the scalar multiplication

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

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

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

- Simplify

Further simplify the matrix.

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

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Short Answer

Step by step solution

- Substitute the matrix

- Perform the scalar multiplication

- Simplify

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91影视

Use matrices A, B, Cand Dto find the following.A=57鈭�163鈭�9,鈥夆赌�B=835144,鈥夆赌�C=04鈭�257鈭�1,鈥夆赌�D=6290鈭�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

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Calculus

Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.