# Vector and Matrix Operations : Row Vectors, Column Vectors, Dot Product and Echelon Form

1. Find the dot product for the following pairs of vectors:

a. Row vector = (2 0) Column vector is below

5

18

b. Row vector = (3 9 -4) Column vector is below

3

0

2

c. Row vector = (5 6 7 8)

1

1

1

1

The following matrices will be used in problems 2-3 below:

0 -2 5

A= 3 -4 17

1 2 3

9 7 2

-3 3 0

B= -4 -5 9

-2 0 6

-8 6 4

3 3 0 -7

X= 7 5 1 1

4 3 3 -1

4 1 0 5

Y= 3 -2 7 1

-5 8 -6 2

2. Answer True or False using the matrices above

a. 2A + 2B = 2(A + B)

b. AT + BT = (A + B)T

c. Let C = A * X, then C will be a 3 by 3 matrix

d. Let D = Y * B, then D will be a 3 by 3 matrix

e. (A * X)T = AT * BT

3. Do the specified matrix multiplications. Show your work.

a. A * X

b. Y * B

c. A * Y

d. B * X

4. Find the inverses of the following matrices

a.

8 6

5 4

b.

3 2

7 4

c.

8 5

-7 -5

d.

3 -4

7 -8

5. Use elementary row operations to reduce the following matrices to echelon or reduced echelon form

a.

0 -2 -1

3 0 0

-1 1 1

b.

3 5 4

1 0 1

2 1 1

c.

3 6 7

0 2 1

2 3 4

Please see the attached file for the fully formatted problems.

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#### Solution Summary

Vector and Matrix Operations, Row Vectors, Column Vectors, Dot Product and Echelon Form are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.