If x[23]+y[-11]=[105], find values of x and y. - Mathematics

Question

if $x [\begin{matrix} 2 \\ 3 \end{matrix}] + y [\begin{matrix} - 1 \\ 1 \end{matrix}] = [\begin{matrix} 10 \\ 5 \end{matrix}]$ , find values of x and y.

Sum

Solution

$x [\frac{2}{3}] + y [\begin{matrix} - 1 \\ 1 \end{matrix}] = [\begin{matrix} 10 \\ 5 \end{matrix}]$

$\Rightarrow [\begin{matrix} 2 x \\ 3 x \end{matrix}] + [\begin{matrix} -y \\ y \end{matrix}] = [\begin{matrix} 10 \\ 5 \end{matrix}]$

$\Rightarrow [\begin{matrix} 2 x - y \\ 3 x + y \end{matrix}] = [\begin{matrix} 10 \\ 5 \end{matrix}]$

Keeping the coefficients of corresponding elements equal,

2x − y = 10 and 3x + y = 5

Adding these two equations, we have:

5x = 15

⇒ x = 3

Now, 3x + y = 5

⇒ y = 5 − 3x

⇒ y = 5 − 9

y = −4

∴ x = 3 and y = −4

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Algebraic Operations on Matrices - Properties of Scalar Multiplication of a Matrix

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Chapter 3: Matrices - Exercise 3.2 [Page 81]

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Chapter 3 Matrices
Exercise 3.2 | Q 11 | Page 81

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If x[23]+y[-11]=[105], find values of x and y. - Mathematics

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