Chapter 4: Q10. (page 164)

Use matrices $A$ , B, and C to find the following.
$A = [\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}], B = [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}], C = [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$
10. $4 A + 2 B - C$

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is

4 A + 2 B - C = [\begin{matrix} - 3 & 30 \\ 26 & 27 \end{matrix}]

Step by step solution

- Substitute the matrices

Substitute $[\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}]$ for A, $[\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}]$ for B and $[\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$ for C into $4 A + 2 B - C$ .

4 A + 2 B - C = 4 [\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}] + 2 [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}] - [\begin{matrix} 9 & - 4 \\ - 6 & 5 \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 first matrix $[\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}]$ by 4 and second matrix $[\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}]$ by 2.

$\begin{matrix} 4 A + 2 B - C = 4 [\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}] + 2 [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}] - [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}] \\ = [\begin{matrix} 4 (2) & 4 (3) \\ 4 (5) & 4 (6) \end{matrix}] + [\begin{matrix} 2 (- 1) & 2 (7) \\ 2 (0) & 2 (4) \end{matrix}] - [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}] \\ = [\begin{matrix} 8 & 12 \\ 20 & 24 \end{matrix}] + [\begin{matrix} - 2 & 14 \\ 0 & 8 \end{matrix}] - [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}] \end{matrix}$

- Perform the matrix addition/subtraction

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

$\begin{matrix} 4 A + 2 B - C = [\begin{matrix} 8 & 12 \\ 20 & 24 \end{matrix}] + [\begin{matrix} - 2 & 14 \\ 0 & 8 \end{matrix}] - [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}] \\ = [\begin{matrix} 8 - 2 - 9 & 12 + 14 - (- 4) \\ 20 + 0 - (- 6) & 24 + 8 - 5 \end{matrix}] \\ = [\begin{matrix} - 3 & 30 \\ 26 & 27 \end{matrix}] \end{matrix}$

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Use matrices $A$ , B, and C to find the following.
$A = [\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}], B = [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}], C = [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$
10. $4 A + 2 B - C$

Short Answer

Step by step solution

- Substitute the matrices

- Perform the scalar multiplication

- Perform the matrix addition/subtraction

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Use matrices A, B, and C to find the following.A=2356, B=−1704, C=9−4−6510. 4A+2B-C

Short Answer

Step by step solution

- Substitute the matrices

- Perform the scalar multiplication

- Perform the matrix addition/subtraction

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Discrete Mathematics

Statistics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use matrices $A$ , B, and C to find the following.
$A = [\begin{matrix} 2 & 3 \\ 5 & 6 \end{matrix}], B = [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}], C = [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$
10. $4 A + 2 B - C$