Q. 295.0( 1 Vote )

# Using matrices, solve the following system of linear equations:

x - y + 2z = 7

3x + 4y - 5z = - 5

2x - y + 3z = 12

**OR**

Using elementary operations, find the inverse of the following matrix:

Answer :

Given; x - y + 2z = 7

3x + 4y - 5z = - 5

2x - y + 3z = 12

∴ AX = B

⇒ X = A ^{- 1}B

|A| = 1(12 − 5) + 1(9 + 10) + 2(−3 − 8)

= 7 + 19 − 22

= 4 ≠ 0

∴ A ^{- 1} exists

Cofactors of A are;

A_{11} = 7 A_{12} = −19 A_{13} = −11

A_{21} = 1 A_{22} = −1 A_{23} = −1

A_{31} = −3 A_{32} = 11 A_{33} = 7

∴ x = 2, y = 1, z = 3 is the Required solution.

**OR**

Given;

A = IA

R_{1}→ 2R_{1} + R_{3}

R_{2}→ R_{2} − R_{1}

R_{2}→ R_{2} − R_{1}

R_{1} → R_{1} + 3R_{2} and R_{3} → R_{3} − 3R_{1}

R_{2} → −R_{2}

R_{3} → R_{3} + 8R_{2}

R_{1} → R_{1} + 1/2 R_{3}

R_{2} → R_{2} − R_{3} and R_{3} → 1/2 R_{3}

Rate this question :

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:

Mathematics - Board Papers

If find A^{2} – 5A – 14I.

If possible, using elementary row transformations, find the inverse of the following matrices

Mathematics - Exemplar

If possible, using elementary row transformations, find the inverse of the following matrices

Mathematics - Exemplar

If f(x) = x^{3} + 4x^{2} – x, find f(A), where

If f(x) = x^{2} – 2x, find f(A), where

Using matrices, solve the following system of linear equations:

x - y + 2z = 7

3x + 4y - 5z = - 5

2x - y + 3z = 12

**OR**

Using elementary operations, find the inverse of the following matrix:

Mathematics - Board Papers

Show that the matrix satisfies the equation A^{3} – 4A^{2} + A = 0.