Q. 265.0( 2 Votes )

# Using matrices, solve the following system of equations:

x + y + z = 6

x + 2z = 7

3x + y + z = 12

**OR**

Obtain the inverse of the following matrix, using elementary operations:

Answer :

Given: equations are x + y + z = 6, x + 2z = 7, 3x + y + z = 12

Given: equation can be written in matrix form as

AX = B ⇒ X = A^{-1}B … (1)

Here

Now |A| = 1 (0 – 2) – 1 (1 – 6) + 1 (1 – 0)

= -2 + 5 + 1

= 4 ≠ 0

∴ A^{-1} exists.

Now for adj A:

⇒ A_{11} = -2

⇒ A_{11} = -(-5) = 5

⇒ A_{11} = 1

⇒ A_{11} = -(1 – 1) = 0

⇒ A_{11} = 1 – 3 = -2

⇒ A_{11} = -(1 – 3) = 2

⇒ A_{11} = 2 – 0 = 2

⇒ A_{11} = -(2 – 1) = -1

⇒ A_{11} = 0 – 1 = -1

From (1), X = A^{-1}B

∴ x = 3, y = 1 and z = 2

**OR**

Given:

∴ A = IA

Applying R_{1}→ 1/3 R_{1}, we get

Applying R2 → R_{2} – 2R_{1}, we get

Applying R_{2}→ 1/3 R_{2}, we get

Applying R_{3}→ R_{3} – 4R_{2}, we get

Applying R_{3}→ 9R_{3}, we get

Applying R_{2}→ R_{2} – 2/9 R_{3} and R_{1}→ 1/3 R_{3}, we get

Rate this question :

Using matrices, solve the following system of equations:

x + y + z = 6

x + 2z = 7

3x + y + z = 12

**OR**

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**OR**

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