Matrices and Determinants, math homework help

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Assignment 12 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 Matrices and Determinants in the College Algebra textbook. Matrices and Determinants For (1) through (10) : Enter T if the answer to the problem is True, otherwise enter F for False. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) _____ The following determinant evaluates to 5 . −5 −2 − 10 −3 _____ The following determinant evaluates to 0 . −1 −1 −1 −1 _____ The following determinant evaluates to 1 . −3 +2 −2 −1 _____ The following determinant evaluates to 0 . −7 −1 −7 −1 _____ The following determinant evaluates to 0 . −6 −6 −5 −5 _____ The following determinant evaluates to 0 . −1 −1 −1 −1 _____ The following determinant evaluates to a −a −b −b −a 2 2 − b . _____ The following determinant evaluates to 1 . −3 +2 −2 −1 _____ The following determinant evaluates to − 33 . −1 −6 −6 −2 −0 −5 −1 −3 −7 _____ The following determinant evaluates to − 248 . −2 −2 −8 −3 −5 −6 −4 −6 −9 © Copyright 2016 by P . E . P . 1 Assignment 12 MATH 140 College Algebra Student Name Section For (11) - (15) : Choose from (a) , (b) , (c) , (d) or (e) to select your answer to the problem. (11) (12) (13) (14) (15) What value of x will make the following matrix determinant true? − 12 −x −2 −3 − − = 12 (a) − 18 (b) 12 (c) 42 (d) 24 (e) What value of x will make the following matrix determinant true? −7 +5 −x −9 − − = −3 16 (a) − 12 (b) 12 (c) 42 (d) 24 (e) 16 A system of two linear equations in two unknowns x and y is represented by the following augmented matrix. What is the solution of the system of equations? −1 −4 −1 −0 −0 −1 −2 −0 (a) x = 9; y = −2 (b) x = 1; y = −5 (c) x = − 7 ; y = − 2 (d) x = −1; y = −2 What is the solution of this 2 by 2 system of equations, represented in matrix form? +1 +1 − 08 −0 −2 +2 − 24 −0 (a) x = 10 ; y = − 2 (b) x = 10 ; y = 2 (c) x = − 2 ; y = 10 (d) x = − 10 ; y = 2 A system of three linear equations in three unknowns x , y and z is represented by the following augmented matrix. What is the solution of the system of equations? +1 +1 +1 − 08 −0 −2 +2 −2 − 16 −0 +3 +5 −1 + 32 −0 (a) x = 10 ; y = 1 ; z = − 2 (c) x = − 2 ; y = 10 ; z = − 2 (b) x = 10 ; y = 0 ; z = − 2 (d) x = − 10 ; y = 0 ; z = − 2 For problems (16) through (25) , refer to the ( x , y , z ) augmented matrix given below. (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) +1 +1 −1 +3 −0 −2 +2 −1 −4 −0 +3 +5 −3 +9 −0 This is a three row and four column augmented matrix. (a) True (b) False This is a four row and three column augmented matrix. (a) True (b) False The top row of the matrix represents the equation: x + y − z = 3 (a) True (b) False The last row of the matrix denotes the equation: 3 x + 5 y − 3 z = 9 (a) True (b) False The augmented matrix is a 4 × 3 dimensional matrix. (a) True (b) False The solution of the underlying system is: x = 1 , y = 0 , z = 2 / 3 (a) True (b) False The solution of the underlying system is: x = 7 / 3 , y = 0 , z = − 2 / 3 (a) True (b) False The above system is in the matrix form A x = B . (a) True (b) False If any two rows of the above augmented matrix would interchange, then the solution to the underlying system would be the same. (a) True (b) False If any two columns of the above augmented matrix would interchange, then the solution to the underlying system would be the same. (a) True (b) False © Copyright 2016 by P . E . P . 2
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