Matrix Algebra

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Assignment 13 MATH 140 College Algebra Student Name Section 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 Points Score 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Total 4 4 4 100 points 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) (2) (3) 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 (c) one - row and three - columns (d) four - rows and six - columns for the given matrix which expression is located in Row 2 , Column 1 ? − 3h − 2m − 6d (a) 3 h (b) 5 f (c) 6 d (d) − 6 d (e) 2 m 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. (a) (4) − 5f Dryers Microwaves Washers April 007 012 015 May 010 005 012 True (b) (6) −5 −6 + −5 3 8 6 a c = b d (a) b = −2 , c = 3 (b) b = 3 , c = 11 (c) b = 11 , c = 11 (d) b = 3,c = 2 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 Find the values of x and y such that the following subtraction of matrix arrays is true. 3 7 (7) False Determine the value of b and c when the following matrices are added. 3 8 (5) Sales Matrix x − −6 −5 8 8 y = 8 −1 4 14 (a) x = 12 , y = 20 (b) x = 12 , y = − 20 (c) x = − 12 , y = 4 (d) x = − 12 , y = 20 Determine the values of x and y such that the following will be true. (a) (c) −5 −3 −9 −6 −8 −5 −3 −6 −x − x = − 10 , y = − 1 x = − 10 , y = 4 © Copyright 2016 by P . E . P . −1 −1 −6 −9 −9 −y −2 −2 −2 (b) (d) −4 = −4 −3 − 3 − 17 −4 −1 −8 −4 x = − 10 , y = 1 x = − 8 , y = 20 1 Assignment 13 MATH 140 College Algebra Student Name (8) Section Given a matrix B and a scalar k , which of these demonstrates scalar multiplication between B and k ? (a) B + k (9) (b) B ÷ k (c) k B (d) k + B −1 (e) B + B −1 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 −5 matrix B −0 × −1 −4 −0 −2 (a) − 6 (11) (b) − 18 (c) − 20 (d) 0 (e) not possible The Quantity Matrix and Price Matrix for the first quarter is given in the matrix below. Quantity Matrix (12) 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 Consider the product of matrix A and matrix B . Determine the row 2 column 2 element in the product matrix A B . matrix A (a) (13) Price Matrix matrix B −5 −0 −1 −2 −4 +5 −1 −1 −2 52 (b) × 13 −4 −3 −7 −0 −2 −3 −2 −1 −1 (c) A matrix B is said to be idempotent if B −2 −1 −3 −2 (a) Yes © Copyright 2016 by P . E . P . 25 2 (d) 6 (e) 7 = B . Is the following matrix idempotent? (b) No 2 Assignment 13 MATH 140 College Algebra Student Name (14) Section What is the value of entry r in the product matrix shown below? −2 5 −7 8 × 9 2 −8 −4 = r t s u (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 . © Copyright 2016 by P . E . P . (a) True (b) False 3
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