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Category > Engineering Posted 19 Aug 2017 My Price 9.00

Matrix Algebra

showing work is not required.

Instructor

Due Date

Exercise	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	Total
Points	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	100G101010 pointsG
Score

Textbook Reading Assignment

Read the chapter section on Functions in the College Algebra textbook.

Matrix Algebra

For (1) - (25) : Choose from (a) , (b) , (c) , (d) or (e) to select your answer to the problem.

(1) A two - row, three - column matrix added to another two - row, three - column matrix yields a sum matrix having a dimension of __________ .

(a) four - rows and nine - columns (b) two - rows and three - columns

(2) for the given matrix which expression is located in Row 2 , Column 1 ?

− 5 f

− 3 h

− 2 m

− 6 d

(a) 3 h (b) 5 f (c) 6 d (d) − 6 d (e) 2 m

(3) The following matrix correctly summarizes the information given below.

An appliance salesperson sold 15 washers, 7 dryers and 13 microwave ovens in April. She sold 12 washers, 10 dryers and 5 microwaves in May.


	Dryers	Microwaves	Washers	Sales Matrix
April	007	012	015
May	010	005	012

(a) True (b) False

(4) Determine the value of b and c when the following matrices are added.

− 5

− 6

(a) b = − 2 , c = 3 (b) b = 3 , c = 11

(5) If A and B are matrices of like dimensions, then matrix subtraction between these matrices is typically commutative, i.e. A − B = B − A .

(a) True (b) False

(6) Find the values of x and y such that the following subtraction of matrix arrays is true.

−

− 5

− 6

− 1

(a) x = 12 , y = 20 (b) x = 12 , y = − 20

(7) Determine the values of x and y such that the following will be true.

− 5

− 3

− 9

− 1

− 6

− 4

− 3

− 6

− 8

− 5

−

− 9

− y

− 3

− 17

− 4

− 3

− 6

− x

− 2

− 1

− 4

− 8

(a) x = − 10 , y = − 1 (b) x = − 10 , y = 1

(8) Given a matrix B and a scalar k , which of these demonstrates scalar multiplication between B and k ?

(a) B + k (b) B ÷ k (c) k B (d) k + B ^{− 1} (e) B + B ^{− 1}

(9) A movie complex has two separate theaters: Cinema 1 and Cinema 2 . The attendance Monday for the entire complex is given in the matrix below.

Adults

Children

Cinema 1

109

105

Cinema 2

172

019

If the admission price for each cinema is $ 5 for children $ 7 for adults, find the total revenue that was collected Monday at the theater complex.

(a) $ 2,587 (b) $ 2,578 (c) $ 2,857 (d) $ 2,758 (e) $ 2,875

(10) Multiply these matrices, if possible

matrix A			matrix B
− 5	− 0	− 1	×	− 4
				− 0
				− 2

(a) − 6 (b) − 18 (c) − 20 (d) 0 (e) not possible

(11) The Quantity Matrix and Price Matrix for the first quarter is given in the matrix below.

	Quantity Matrix			Price Matrix
	Item 1	Item 2	Item 3
January	028	075	520	Item 1	$ 3.00
February	029	243	182	Item 2	$ 2.50
March	101	240	019	Item 3	$ 1.25

Which month yields the greatest Quantity × Price amount?

(a) January (b) February (c) March (d) April (e) May

(12) Consider the product of matrix A and matrix B . Determine the row 2 column 2 element in the product matrix A B .

matrix A

matrix B

− 5

− 0

− 1

− 4

− 3

− 7

− 2

− 4

+ 5

− 0

− 2

− 3

− 1

− 2

− 1

(a) 52 (b) 13 (c) 25 (d) 6 (e) 7

(13) A matrix B is said to be idempotent if B ² = B . Is the following matrix idempotent?

− 2

− 1

− 3

− 2

(a) Yes (b) No

(14) What is the value of entry r in the product matrix shown below?

− 2

− 7

− 8

− 4

(a) r = − 2 (b) r = 7 (c) r = − 18 (d) r = − 32 (e) r = − 20

For problems (15) through (20) , refer to the matrix arrays given below.

matrix X		matrix Y
+ 5	− 0	− 8	− 6
− 3	− 1	− 5	− 9
− 1	+ 4	− 8	− 4

(15) The matrix sum X + Y is defined and is possible to compute. (a) True (b) False

(16) The matrix product X × Y is NOT defined. (a) True (b) False

(17) The matrix product Y × X is defined. (a) True (b) False

(18) The trace of matrix Y is 16 . (a) True (b) False

(19) In reduced row - echelon form, Y has diagonal elements of 1 and 0.50 . (a) True (b) False

(20) When Y is multiplied by its transpose, the product is the identity matrix. (a) True (b) False

For problems (21) through (25) , refer to the matrix arrays given below.

matrix X

matrix Y

+ 7

− 5

− 8

− 7

− 5

− 6

− 5

− 0

+ 3

− 5

− 0

− 9

− 6

+ 9

− 4

− 8

− 3

− 4

(21) The matrix sum X + Y is not possible to compute. (a) True (b) False

(22) The matrix product X × Y is defined. (a) True (b) False

(23) The trace of Matrix X is greater than the trace of Matrix Y . (a) True (b) False

(24) Matrix Y is the transpose of Matrix X . (a) True (b) False

(25) If I ₃ represents the 3 × 3 Identity matrix, then Y × I ₃ = I ₃ . (a) True (b) False

Answers

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Status NEW Posted 19 Aug 2017 07:08 AM My Price 9.00

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