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CBSE Class 12 · 2007 · MatricesLong Answer

Using matrices, solve the following system of equations:

x + 2 y - 3 z = 6, 3 x + 2 y - 2 z = 3, 2 x - y + z = 2.

Answer: $x = 1, y = - 5, z = - 5$ \,

Solution

Form

A X = B

with

A = 132 22 - 1 - 3 - 2 1

,

B = 632

. Here

∣ A ∣ = 7 \neq = 0

, so

X = A^{- 1} B

with

A^{- 1} = \frac{1}{7} 0 - 7 - 7 175 2 - 7 - 4

.

X = \frac{1}{7} 7 - 35 - 35 = 1 - 5 - 5 .

x = 1, y = - 5, z = - 5

Check: equation 2 gives

3 (1) + 2 (- 5) - 2 (- 5) = 3

and equation 3 gives

2 (1) - (- 5) + (- 5) = 2

(both hold); equation 1 gives

1 + 2 (- 5) - 3 (- 5) = 6

(holds).

CBSE Class 12 Board · 2007 · Subjective

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