Chapter 4: Q9. (page 164)

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

Short Answer

Expert verified

The final matrix after performing the indicated matrix operations is

$3 B - 2 C = [\begin{matrix} - 21 & 29 \\ 12 & 2 \end{matrix}]$ .

Step by step solution

- Substitute the matrices

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

$3 B - 2 C = 3 [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}] - 2 [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$

- 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 $[\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}]$ by 3 and multiply each element of the second matrix $[\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}]$ by 2.

$\begin{matrix} 3 B - 2 C = 3 [\begin{matrix} - 1 & 7 \\ 0 & 4 \end{matrix}] - 2 [\begin{matrix} 9 & - 4 \\ - 6 & 5 \end{matrix}] \\ = [\begin{matrix} 3 (- 1) & 3 (7) \\ 3 (0) & 3 (4) \end{matrix}] - [\begin{matrix} 2 (9) & 2 (- 4) \\ 2 (- 6) & 2 (5) \end{matrix}] \\ = [\begin{matrix} - 3 & 21 \\ 0 & 12 \end{matrix}] - [\begin{matrix} 18 & - 8 \\ - 12 & 10 \end{matrix}] \end{matrix}$

- Perform the matrix subtraction

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

$\begin{matrix} 3 B - 2 C = [\begin{matrix} - 3 & 21 \\ 0 & 12 \end{matrix}] - [\begin{matrix} 18 & - 8 \\ - 12 & 10 \end{matrix}] \\ = [\begin{matrix} - 3 - 18 & 21 - (- 8) \\ 0 - (- 12) & 12 - 10 \end{matrix}] \\ = [\begin{matrix} - 21 & 29 \\ 12 & 2 \end{matrix}] \end{matrix}$

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

Short Answer

Step by step solution

- Substitute the matrices

- Perform the scalar multiplication

- Perform the matrix subtraction

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Use matricesA, B, and C to find the following.A=2356, B=−1704, C=9−4−659. 3B-2C

Short Answer

Step by step solution

- Substitute the matrices

- Perform the scalar multiplication

- Perform the matrix subtraction

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Mechanics Maths

Discrete Mathematics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

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