If [2x+y4x5x-74x]=[77y-13yx+6], then the value of x + y is ______. - Mathematics

Question

If $[\begin{matrix} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{matrix}] = [\begin{matrix} 7 & 7 y - 13 \\ y & x + 6 \end{matrix}]$ , then the value of x + y is ______.

Options

x = 3, y = 1
x = 2, y = 3
x = 2, y = 4
x = 3, y = 3

MCQ

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Solution

If $[\begin{matrix} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{matrix}] = [\begin{matrix} 7 & 7 y - 13 \\ y & x + 6 \end{matrix}]$ , then the value of x + y is x = 2, y = 3.

Explanation:

Given that: $[\begin{matrix} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{matrix}] = [\begin{matrix} 7 & 7 y - 13 \\ y & x + 6 \end{matrix}]$

Equating the corresponding elements, we get,

2x + y = 7 ......(i)

And 4x = x + 6 ......(ii)

From equations (ii)

4x – x = 6

3x = 6

∴ x = 2

From equations (i)

2 × 2 + y = 7

4 + y = 7

∴ y = 7 – 4 = 3

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Q 55 Q 54 Q 56

Chapter 3: Matrices - Exercise [Page 59]

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Chapter 3 Matrices
Exercise | Q 55 | Page 59

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If [2x+y4x5x-74x]=[77y-13yx+6], then the value of x + y is ______. - Mathematics

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