Question

solve matrix [3 1 5 2]x=[-1 2 3 1]

Answer 1

Answer:

Let A=[

a

b

c

d

]

so, [

2

3

1

2

]A[

−3

5

2

−3

]=[

1

0

0

1

]

⇒[

2

3

1

2

][

a

b

c

d

][

−3

5

2

−3

]=[

1

0

0

1

]

⇒[

2a+b

3a+2b

2c+d

3c+2d

][

−3

5

2

−3

][

1

0

0

1

]

⇒[

−6a−3b+10c+5d

−9a−6b+15c+10d

4a+3b−6c−3d

6a+4b−9c−6d

]=[

1

0

0

1

]

so, −6a−3b+10c+5d=1

4a+3b−6c−3d=0

−9a−6b+15c+10d=0

6a+4b−9c−6d=1

on squaring, we get

⇒a=

3

1

,b=1,c=

3

1

,d=

15

8

so, A=

⎣

⎢

⎢

⎡

3

1

0

3

1

15

8

⎦

⎥

⎥

⎤

=

15

1

[

5

15

5

8

].

Hence, the answer is

15

1

[

5

15

5

8

]

Answer 2

Concept:

Here, we will find the matrix by taking matrix on left side to right side by taking its inverse.

Given:

A = $\left[\begin{array}{ccc}3&1\\5&2\\\end{array}\right]$  & B = $\left[\begin{array}{ccc}-1&2\\3&1\\\end{array}\right]$

Find:

Matrix X

Solution:

AX = B ⇒ X = B A$^{-1}$

Adj A = $\left[\begin{array}{ccc}1&-4\\-1&5\\\end{array}\right]$

inv A = $\left[\begin{array}{ccc}1&-4\\-1&5\\\end{array}\right]$

X = B x inv (A)

X = $\left[\begin{array}{ccc}-1&2\\3&1\\\end{array}\right]$ x $\left[\begin{array}{ccc}1&-4\\-1&5\\\end{array}\right]$

X = $\left[\begin{array}{ccc}-3&-14\\4&17\\\end{array}\right]$

Thus, the value of X is $\left[\begin{array}{ccc}-3&-14\\4&17\\\end{array}\right]$

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