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CBSE Class 12 · 2019 · MatricesLong Answer

Using the matrix method, solve the following system of equations:

3 x - 2 y + 3 z = 8, 2 x + y - z = 1, 4 x - 3 y + 2 z = 4.

Answer: $x = 1, y = 2, z = 3$

Solution

Form

A X = B

with

A = 324 - 2 1 - 3 3 - 1 2

,

B = 814

. Here

∣ A ∣ = - 17 \neq = 0

, so a unique solution exists.
Solving (e.g.

X = A^{- 1} B

, or elimination: from eq.2

y = 1 - 2 x + z

) gives

x = 1, y = 2, z = 3.

Check:

3 - 4 + 9 = 8

,

2 + 2 - 3 = 1

,

4 - 6 + 6 = 4

.

x = 1, y = 2, z = 3

CBSE Class 12 Board · 2019 · Subjective

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