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.