Find the value of x, y, and z from the following equation: [x+y25+zxy]=[6258] - Mathematics

प्रश्न

Find the value of x, y, and z from the following equation:

$[\begin{matrix} x + y & 2 \\ 5 + z & x y \end{matrix}] = [\begin{matrix} 6 & 2 \\ 5 & 8 \end{matrix}]$

बेरीज

उत्तर

$[\begin{matrix} x + y & 2 \\ 5 + z & x y \end{matrix}] = [\begin{matrix} 6 & 2 \\ 5 & 8 \end{matrix}]$

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

Comparing the corresponding elements, we get:

Now, 5 + z = 5 ⇒ z = 0

Also, x + y = 6

y = 6 - x .....(i)

and xy = 8 .....(ii)

Solving (i) & (ii), we have x (6 - x) = 8

= 6x - x² = 8

x² - 6x + 8 = 0

= (x - 4) (x - 2) = 0

= x = 2, 4

When x = 2, we get y = 4 and when x = 4, we get y = 6 - 4 = 2

Hence, x = 2, y = 4, z = 0 or x = 4, y = 2, z = 0.

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Types of Matrices

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Q 6.2 Q 6.1 Q 6.3

पाठ 3: Matrices - Exercise 3.1 [पृष्ठ ६४]

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Exercise 3.1 | Q 6.2 | पृष्ठ ६४

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Find the value of x, y, and z from the following equation: [x+y25+zxy]=[6258] - Mathematics

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Find the value of x, y, and z from the following equation: [x+y25+zxy]=[6258] - Mathematics

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