X + Y = 1 X + Z = − 6 X − Y − 2z = 3 - Mathematics

प्रश्न

x + y = 1
x + z = − 6
x − y − 2z = 3

योग

उत्तर

These equations can be written as
x+ y + 0z = 1
x + 0y + z = − 6
x − y − 2z = 3

$D = | \begin{matrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & - 1 & - 2 \end{matrix} |$

$= 1 (0 + 1) - 1 (- 2 - 1) + 0 (- 1 - 0)$

$= 4$

$D_{1} = | \begin{matrix} 1 & 1 & 0 \\ - 6 & 0 & 1 \\ 3 & - 1 & - 2 \end{matrix} |$

$= 1 (0 + 1) - 1 (12 - 3) + 0 (6 - 0)$

$= - 8$

$D_{2} = | \begin{matrix} 1 & 1 & 0 \\ 1 & - 6 & 1 \\ 1 & 3 & - 2 \end{matrix} |$

$= 1 (12 - 3) - 1 (- 2 - 1) + 0 (3 + 6)$

$= 12$

$D_{3} = | \begin{matrix} 1 & 1 & 1 \\ 1 & 0 & - 6 \\ 1 & - 1 & 3 \end{matrix} |$

$= 1 (0 - 6) - 1 (3 + 6) + 1 (- 1 - 0)$

$= - 16$

$Now,$

$x = \frac{D_{1}}{D} = \frac{- 8}{4} = - 2$

$y = \frac{D_{2}}{D} = \frac{12}{4} = 3$

$z = \frac{D_{3}}{D} = \frac{- 16}{4} = - 4$

$∴ x = - 2, y = 3 and z = - 4$

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Applications of Determinants and Matrices

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Q 18 Q 17 Q 19

अध्याय 6: Determinants - Exercise 6.4 [पृष्ठ ८४]

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अध्याय 6 Determinants
Exercise 6.4 | Q 18 | पृष्ठ ८४

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X + Y = 1 X + Z = − 6 X − Y − 2z = 3 - Mathematics

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X + Y = 1 X + Z = − 6 X − Y − 2z = 3 - Mathematics

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