3x − Y + 2z = 3 2x + Y + 3z = 5 X − 2y − Z = 1 - Mathematics

Question

3x − y + 2z = 3
2x + y + 3z = 5
x − 2y − z = 1

Solution

Given: 3x − y + 2z = 3
2x + y + 3z = 5
x − 2y − z = 1

$D = | \begin{matrix} 3 & - 1 & 2 \\ 2 & 1 & 3 \\ 1 & - 2 & - 1 \end{matrix} |$
$= 3 (- 1 + 6) + 1 (- 2 - 3) + 2 (- 4 - 1)$
$= 0$
$D_{1 =} | \begin{matrix} 3 & - 1 & 2 \\ 5 & 1 & 3 \\ 1 & - 2 & - 1 \end{matrix} |$
$= 3 (- 1 + 6) + 1 (- 5 - 3) + 2 (- 10 - 1)$
$= - 15$
$D_{2} = | \begin{matrix} 3 & 3 & 2 \\ 2 & 5 & 3 \\ 1 & 1 & - 1 \end{matrix} |$
$= 3 (- 5 - 3) - 3 (- 2 - 3) + 2 (2 - 5)$
$= - 15$
$D_{3} = | \begin{matrix} 3 & - 1 & 3 \\ 2 & 1 & 5 \\ 1 & - 2 & 1 \end{matrix} |$
$= 3 (1 + 10) + 1 (2 - 5) + 3 (- 4 - 1)$
$= - 15$ Here, D is zero, but D₁, D₂ and D₃ are non-zero. Thus, the system of linear equations is inconsistent.

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Applications of Determinants and Matrices

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Q 24 Q 23 Q 25

Chapter 6: Determinants - Exercise 6.4 [Page 84]

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Chapter 6 Determinants
Exercise 6.4 | Q 24 | Page 84

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3x − Y + 2z = 3 2x + Y + 3z = 5 X − 2y − Z = 1 - Mathematics

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