Chapter 4: Q43. (page 166)

Solve for x and y in the matrix equation $[\begin{matrix} x \\ 7 \end{matrix}] + [\begin{matrix} 3 y \\ - x \end{matrix}] = [\begin{matrix} 16 \\ 12 \end{matrix}]$

Short Answer

Expert verified

The values of x and y in the matrix equation $[\begin{matrix} x \\ 7 \end{matrix}] + [\begin{matrix} 3 y \\ - x \end{matrix}] = [\begin{matrix} 16 \\ 12 \end{matrix}]$ is $(- 5, 7)$ .

Step by step solution

- Define concept of matrix addition

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

- Add corresponding elements

In order to find x, first add corresponding elements of both the matrices

$[\begin{matrix} x \\ 7 \end{matrix}] + [\begin{matrix} 3 y \\ - x \end{matrix}] .$

$\begin{matrix} [\begin{matrix} x \\ 7 \end{matrix}] + [\begin{matrix} 3 y \\ - x \end{matrix}] = [\begin{matrix} 16 \\ 12 \end{matrix}] \\ [\begin{matrix} x + 3 y \\ 7 - x \end{matrix}] = [\begin{matrix} 16 \\ 12 \end{matrix}] \end{matrix}$

- Equate the matrix

In order to find the values of x and y, equate the corresponding elements since the two matrices are equal therefore, there corresponding elements will also be equal.

$x + 3 y = 16$ … (i)

$7 - x = 12$ …(ii)

- Solve for x and y

Solve equation (ii) for x and get,

$\begin{matrix} 7 - x - 7 = 12 - 7 \\ - x = 5 \\ - x \times (- 1) = 5 \times (- 1) \\ x = - 5 \end{matrix}$

Substitute -5 for x into equation (i) and solve for y.

$\begin{matrix} (- 5) + 3 y = 16 \\ (- 5) + 3 y + 5 = 16 + 5 \\ \frac{3 y}{3} = \frac{21}{3} \\ y = 7 \end{matrix}$

Therefore, the solution of the matrix is $(- 5, 7)$ .

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Solve for x and y in the matrix equation $[\begin{matrix} x \\ 7 \end{matrix}] + [\begin{matrix} 3 y \\ - x \end{matrix}] = [\begin{matrix} 16 \\ 12 \end{matrix}]$

Short Answer

Step by step solution

- Define concept of matrix addition

- Add corresponding elements

- Equate the matrix

- Solve for x and y

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Solve for x and y in the matrix equationx7+3y−x=1612

Short Answer

Step by step solution

- Define concept of matrix addition

- Add corresponding elements

- Equate the matrix

- Solve for x and y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Calculus

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve for x and y in the matrix equation $[\begin{matrix} x \\ 7 \end{matrix}] + [\begin{matrix} 3 y \\ - x \end{matrix}] = [\begin{matrix} 16 \\ 12 \end{matrix}]$