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Find the Value Of X, Y, And Z From the Following Equation [(X+Y, 2),(5+Z, Xy)] = [(6,2), (5,8)] - CBSE (Science) Class 12 - Mathematics

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Question

Find the value of xy, and z from the following equation:

`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`

Solution

`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`

As the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding elements, we get:

x + y = 6, xy = 8, 5 + = 5

Now, 5 + z = 5 ⇒ z = 0

We know that:

(x − y)2 = (x + y)2 − 4xy

⇒ (x − y)2 = 36 − 32 = 4

⇒ x − y = ±2

Now, when x − y = 2 and x + y = 6, we get x = 4 and y = 2

When x − = − 2 and x + y = 6, we get x = 2 and = 4

x = 4, y = 2, and z = 0 or x = 2, y = 4, and z = 0

 

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Solution Find the Value Of X, Y, And Z From the Following Equation [(X+Y, 2),(5+Z, Xy)] = [(6,2), (5,8)] Concept: Types of Matrices.
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