Using matrices solve the following system of linear equations:
x - y + 2 z = 7
3 x + 4 y - 5 z = - 5
2 x - y + 3 z = 12

Solution

The given system of equation can be written in the form of AX = B, where

$A = [\begin{matrix} 1 & - 1 & 2 \\ 3 & 4 & - 5 \\ 2 & - 1 & 3 \end{matrix}], X = [\begin{matrix} x \\ y \\ z \end{matrix}] and B = [\begin{matrix} 7 \\ - 5 \\ 12 \end{matrix}] .$

Now,

$|A| = 1 (12 - 5) + 1 (9 + 10) + 2 (- 3 - 8) = 7 + 19 - 22 = 4 \neq 0$

Thus, A is non-singular. Therefore, its inverse exists.

Now, A₁₁ = 7, A₁₂ = - 19, A₁₃ = - 11

A₂₁ = 1, A₂₂ = - 1, A₂₃ = - 1

A₃₁ = - 3, A₃₂ = 11, A₃₃ = 7

$∴ A^{- 1} = \frac{1}{|A|} (adj A) = \frac{1}{4} [\begin{matrix} 7 & 1 & - 3 \\ - 19 & - 1 & 11 \\ - 11 & - 1 & 7 \end{matrix}]$

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Relations And Functions

Using matrices solve the following system of linear equations:
x - y + 2 z = 7
3 x + 4 y - 5 z = - 5
2 x - y + 3 z = 12

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Relations And Functions

Using matrices solve the following system of linear equations:x - y + 2 z = 73 x + 4 y - 5 z = - 52 x - y + 3 z = 12

Some More Questions From Relations and Functions Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Using matrices solve the following system of linear equations:
x - y + 2 z = 7
3 x + 4 y - 5 z = - 5
2 x - y + 3 z = 12