# Using matrices, solve the following system of equations:x + y + z = 6x + 2z = 73x + y + z = 12ORObtain the inverse of the following matrix, using elementary operations:

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-1B … (1)

Here

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

= -2 + 5 + 1

= 4 ≠ 0

A-1 exists.

A11 = -2

A11 = -(-5) = 5

A11 = 1

A11 = -(1 – 1) = 0

A11 = 1 – 3 = -2

A11 = -(1 – 3) = 2

A11 = 2 – 0 = 2

A11 = -(2 – 1) = -1

A11 = 0 – 1 = -1

From (1), X = A-1B

x = 3, y = 1 and z = 2

OR

Given:

A = IA

Applying R1 1/3 R1, we get

Applying R2 R2 – 2R1, we get

Applying R2 1/3 R2, we get

Applying R3 R3 – 4R2, we get

Applying R3 9R3, we get

Applying R2 R2 – 2/9 R3 and R1 1/3 R3, we get

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