Q. 274.5( 2 Votes )

# Solve the following questions.

, find A ^{– 1} and hence solve the following system of equations:

3x – 4y + 2z = – 1, 2x + 3y + 5z = 7, x + z = 2.*(CBSE 2011)*

*(CBSE 2011)*

Answer :

A =

|A| = 3(3 – 0) + 4(2 – 5) + 2(0 – 3)

= 9 – 12 – 6

= – 9

Now, the cofactors of A

**C _{11}** = (– 1)

^{1 + 1}3 – 0 = 3

**C _{21}** = (– 1)

^{2 + 1}– 4 – 0 = 4

**C _{31}** = (– 1)

^{3 + 1}– 20 – 6 = – 26

**C _{12}** = (– 1)

^{1 + 2}2 – 5 = 3

**C _{22}** = (– 1)

^{2 + 1}3 – 2 = 1

**C _{32}** = (– 1)

^{3 + 1}15 – 4 = – 11

**C _{13}** = (– 1)

^{1 + 2}0 – 3 = – 3

**C _{23}** = (– 1)

^{2 + 1}0 + 4 = – 4

**C _{33}** = (– 1)

^{3 + 1}9 + 8 = 17

adj A =

A ^{– 1 =}

A ^{– 1} =

Now the given equation can be written as:

A X B

Or, X = A ^{– 1}B

=

X =

X =

Hence, x = 3,y = 2 and z = – 1

Rate this question :

Using matrices, solve the following system of equations:

2x + 3y + 3z = 5, x – 2y + z = – 4, 3x – y – 2z = 3

Mathematics - Board PapersIf find Using solve the system of equation

Mathematics - Board PapersSolve for using properties of determinants.

**OR**

Using elementary row operations find the inverse of a matrix and hence solve the following system of equations

Mathematics - Board Papers