Matrices Worksheet 1 - Practice PDF

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Name: __________ Section I. About Matrices. For the following five matrices match them with the correct description on the right. A description may be used once, more than once or not at all. Each matrice has one or more descriptions.

 0 5   A   3 6   1 2

B  8

 3

2  3 1 C  4 2  5 

A. A square matrix B. Row Matrix C. Column Matrix D. Has Element d32 E. A 2 x 1 matrix F. Has 6 elements

 4 2 2 D   0 3 1  2 1 0 

G. A Rectangular Matrix H. A 3 x 2 Matrix

Answer the following questions based on the matrices in the question above. 1. What is the dimension of [C}?

2. Element c12 is _______________ 3. What is the dimension of [B]?

4. Can you add any of the matrices above with another matrix?

5. Can you add any of the matrices with themselves?

Sec II. Add, Subtract, Scalar multiplication. 1. Which matrix could be subtracted from C2x4? a. A4x2

b. A4x3

c. A2x4

d. A2x3

2. In question one above what would the dimensions of the resulting matrix be?

For the next 3 questions use the following matrix equation.  1 2   -2   1 2

 m n 7  6   1 2 =   2    k 

3. The value of k is a. – 1

b. – 3

c. 2

d. – 2

c. 2

d. 1

4. The value of n is a. 4

b. 3

5. Find the value of m

Sec III. Matrix Multiplication 1. Is Matrix multiplication possible for the following matrices? Explain why or why not?

a)

f a b c  e  x   b c d d  

a b   c

 0 5 b)  3 6 x 8  3     1 2

For the next 3 questions use the following matrices.

 0 5   A   3 6   1 2

2  3 1 C  4 2  5 

B  8  3

 20 10  25   D   x 3  33  6 y  9 

2. Is the matrix multiplication of [A] x [C] legal?

3. Which of are legal multiplications?

a) [B] x [C] b) [A] x [D] c) [D] x [C] d) all of the above 4. If the resultant matrix from [A] x [C] is the matrix [D] then what is (x)(y)? a. 30

b. 210

c. -30

d. -64

5. In which of the following matrices can A2 be found. a. b. c. d.

Matrix whose dimensions are 2 x 3. Matrix whose dimensions are 2 x 4 Matrix whose dimensions are 4 x 4 None of the above.

Add the following matrices. 1.

5 8 -2 0 4 -1 3 1 0

+

3 -2 4 -4 2 3 7 -8 4

2.

-1 0 2 1 4 -3

+

5 -2 -1 1 -3 2

-1 0 2 1 4 -3

-

5 -2 -1 1 -3 2

- 2

5 -2 -1 1 -3 2

Subtract the following matrices. 3.

5 8 -2 0 4 -1 3 1 0

-

3 -2 4 -4 2 3 7 -8 4

4.

Multiply the following matrices. 5.

5 8 -2

0

-2

6.

4 -1

3 1

-1 0 1 2

0

2 1 4 -3

Simplify the following expression. 7. -3

5 8 -2 0 4 -1 3 1 0

+ 5

3 -2 4 -4 2 3 7 -8 4

8. 2

-1 0 2 1 4 -3...