- Have you heard of Reginald Denny or Rodney King?

(a) yes

(b) no

(c) unsure

- What size is this matrix?
Matrix([[6,11,-2],[23,31,5]])

(a) 2x3

(b) 3x2

(c) 6

- Let A=Matrix([[4,6],[20,7]. What is 5A?

(a) Matrix([[9,6].[20,7]])

(b) Matrix([9,11],[35,12]])

(c) Matrix([20,6],[20,7]])

(d) Matrix([[20,30],[100,35]])

- Let
A=Matrix([[4,6],[20,24]]) and B=Matrix([[2,5],[3,7]]). What is A+B?

(a) 71

(b) Matrix([[6,9],[7,11]])

(c) Matrix([[6,11],[23,31]])

(d) Matrix([[4,6,2,5],[20,24,3,7]])

- A fruit grower raises two crops, which are shipped to three outlets.
The number of units of Product i that is shipped to Outlet j is represented
by a_ij in the matrix

A:=Matrix([[100 75 75], [125 150 100]]).

The profit of one unit of Product i is represented by b_1i in the matrix

B:=Matrix([[$3.75 $7.00]])

Does the matrix multiplication AB make sense?

a) yes and I have a good reason why

b) yes but I am unsure of why

c) no but I am unsure of why not

d) no and I have a good reason of why not - What can you say about BA, given A and B as in #5?

a) BA is not defined

b) BA is a column vector in R^{2}

c) BA is a column vector in R^{3}

d) BA has an entry consisting of 3.75*100 + 3.75*125

e) BA is defined but none of the above are true

- There exists a matrix A:=Matrix([[a,b],[c,d]]) so that

Matrix([[1,2],[1,2]]) A = Matrix([[1,1],[1,1]])

a) there is exactly 1 matrix A that works.

b) there are infinitely many matrices A that work.

c) there are no matrices that work

d) none of the above

- Which of the following are true?

a) Matrix([[1,0,0],[3,1,0],[0,0,1]]).A is the same as modifying A via r_{2}' = 3 r_{1}+ r_{2}

b)To find an elementary matrix we can apply the row operation to I

c) The inverse of A is the product of the elementary matrices that reduce A to I [so the inverse is E_{k}... E_{2}E_{1}]

d) all of the above

e) more than one of a), b) and c) but not all of them

- There exists a matrix A:=Matrix([[a,b],[c,d]]) so that

A *Matrix([[1,1],[1,1]]) = Matrix([[1,2],[1,2]])

a) there is exactly 1 matrix A that works.

b) there are infinitely many matrices A that work.

c) there are no matrices that work

d) none of the above

- If A=Matrix([[2,3,1],[0,-1,3],[-2,0,4]]) what is A
^{T}?

a) Matrix([[2,3,1],[0,-1,3],[-2,0,4]])

b) Matrix([[2,0,-2],[3,-1,0],[1,3,4]])

c) Matrix([[-2,0,4],[0,-1,3],[2,3,1]])

d) Matrix([[1,3,4],[3,-1,0],[2,0,-2]])

d) None of the above

- You have a business that sells tables and chairs. You have brown tables and
white
tables, and corresponding chairs. Your May sales are 4 brown tables, 6 white
tables, 20
brown chairs, and 24 white chairs, which is represented by the matrix M =
Matrix([[4,6],[20,24]]) where the first row is tables, the second row is
chairs, the first column is brown items, and the second column is white items.
Your June sales are given by the matrix J where J=Matrix([[6,8],[22,32]]).
Which of the following matrix operations would make sense in real life
in this scenario?
Be prepared why or why not.

(a) M+J

(b) M-J

(c) 1.2J

(d) MJ

(e) More than one of the above makes sense.

Solutions

1. a)

2. a)

3. d)

4. c)

5. d)

6. e)

7. b)

8. d)

9. c)

10. b)

11. e) [a, b, c]