This HW all about Matrix and Vector Operations (show all your work please)

please find attached file ðŸ™‚

Numerical and Computer Tools 1 – Homework 1

Matrix and Vector Operations (show all your work)

3

1) ( 5

âˆ’2

6

3

1

âˆ’3) âˆ’ (âˆ’2 âˆ’3) =

7

9

5

2)

2

7 6

5

3

2

(âˆ’6 âˆ’1 âˆ’3) + (âˆ’2 âˆ’3 4) =

4

8 6

0

7 âˆ’1

3)

2

4

8

3 âˆ’5

[âˆ’7 0 ] + [ 10 âˆ’6 âˆ’7] =

âˆ’3 0

3

3

2

4)

4

âˆ’2 2 âˆ’2 âˆ’7

(

) x (âˆ’3

0

5 0 3

4

âˆ’5

5)

âˆ’3

( 7 2 âˆ’ 3) x ( 4 ) =

2

6)

(

2

âˆ’7) =

3

4

4 11 0

2 âˆ’3 5

)x(

)=

16 âˆ’9 1

6 âˆ’4 8

For questions 7, 8 and 9, find the transpose.

7)

2 3 âˆ’3

A = (4 1 âˆ’7) , AT =

5 2 8

8)

2 3 4 âˆ’5 9

A = ( 6 1 3 2 5 ) , AT =

0 4 2 âˆ’1 6

9)

a = [âˆ’2 7 âˆ’19] , aT =

10)

Find ATA for the following matrix. What types of matrix are the result? (Hint: the matrix

is of 2 types)

11)

A=(

2 1 0

)

3 âˆ’2 1

A=(

1 âˆ’2 4

). Show that AI = A and IA = A.

3 7 âˆ’1