Question

find the following of the matrices A= [(1 1 -1 3) (2 -2 6 8) (3 5 -7 8)]​

Answer 1

Answer:

(i) Let A=[

3

1

5

−1

], then A

′

=[

3

5

1

−1

]

Now, A+A

′

=[

3

1

5

−1

]+[

3

5

1

−1

]=[

6

6

6

−2

]

Let P=

2

1

(A+A

′

)=

2

1

[

6

6

6

−2

]=[

3

3

3

−1

]

Now, P

′

=[

3

3

3

−1

]=P

Thus, P=

2

1

(A+A

′

) is a symmetric matrix.

Now, A−A

′

=[

3

1

5

−1

]−[

3

5

1

−1

]=[

0

−4

4

0

]

Let Q=

2