Question

What is the solution of the given matrix equation? [3 1
5 2]

Answer 1

Answer:

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>>Find the matrix A satisfying the matrix

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Find the matrix A satisfying the matrix equation [

2

3

1

2

]A[

−3

5

2

−3

]=[

1

0

0

1

]

Medium

Solution

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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

ANSWER:

The solution of the matrix will be $1$.

Step-by-step explanation:

Given: The matrix $\left[\begin{array}{cc}3&1\\5&2\end{array}\right]$

To find The value of the matrix.

Solution:

• Let the matrix be denoted by A.
• A $=$ $\left[\begin{array}{cc}3&1\\5&2\end{array}\right]$
• Let a $=3$
• b $=1$
• c$=5$
• d$=2$
• We need to first write the matrix in the form of the determiner which will be IAI = (da-bc)
• IAI = ($2$×$3-1$×$5)$
• IAI =$6-5 = 1$
• Therefore, the value of the matrix is $1.$

PROJECT CODE: #SPJ2

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