Find the value of x, y, and z from the following equation: [x+y+zx+zy+z]=[957] - Mathematics

Question

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

$[\begin{matrix} x + y + z \\ x + z \\ y + z \end{matrix}] = [\begin{matrix} 9 \\ 5 \\ 7 \end{matrix}]$

Sum

Solution

$[\begin{matrix} x + y + z \\ x + z \\ y + z \end{matrix}] = [\begin{matrix} 9 \\ 5 \\ 7 \end{matrix}]$

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

Comparing the corresponding elements, we get:

x + y + z = 9 … (1)

x + z = 5 … (2)

y + z = 7 … (3)

From (1) and (2), we have:

y + 5 = 9

⇒ y = 4

Then, from (3), we have:

4 + z = 7

⇒ z = 3

∴ x + z = 5

⇒ x = 2

∴ x = 2, y = 4, and z = 3

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Types of Matrices

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Q 6.3 Q 6.2 Q 7

Chapter 3: Matrices - Exercise 3.1 [Page 64]

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Chapter 3 Matrices
Exercise 3.1 | Q 6.3 | Page 64

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Find the value of x, y, and z from the following equation: [x+y+zx+zy+z]=[957] - Mathematics

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