Q. 294.7( 3 Votes )

# Solve the following system of equations by matrix method:

x – y + 2z = 7

3x + 4y – 5z = – 5

2x – y + 3z = 12 *(CBSE 2012)*

*(CBSE 2012)*

Answer :

The given system can be written in matrix form as:

A X = B

Now,

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

= 7 + 19 – 22

= 4

So, the above system has a unique solution, given by

X = A ^{– 1}B

Cofactors of A are:

**C _{11}** = (– 1)

^{1 + 1}12 – 5 = 7

**C _{21}** = (– 1)

^{2 + 1}– 3 + 2 = 1

**C _{31}** = (– 1)

^{3 + 1}5 – 8 = – 3

**C _{12}** = (– 1)

^{1 + 2}9 + 10 = – 19

**C _{22}** = (– 1)

^{2 + 1}3 – 4 = – 1

**C _{32}** = (– 1)

^{3 + 1}– 5 – 6 = 11

**C _{13}** = (– 1)

^{1 + 2}– 3 – 8 = – 11

**C _{23}** = (– 1)

^{2 + 1}– 1 + 2 = – 1

**C _{33}** = (– 1)

^{3 + 1}4 + 3 = 7

adj A =

=

A ^{– 1} =

Now, X = A ^{– 1}B =

X =

Hence, X = 2,Y = 1 and Z = 3

Rate this question :

If write the cofactor of the element a32 .

Mathematics - Board PapersFind the minor of the element of second row and third column (a_{23}) in the following determinant:

Mathematics - Board Papers

If write the minor of element a_{22}.

Fill in the blanks

If A is a matrix of order 3 × 3, then number of minors in determinant of A are ___.

Mathematics - ExemplarIf write the minor of the element a_{23}.