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Matrices and Determinants,

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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 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) _____ The following determinant evaluates to 5 .

− 5

− 2

− 10

− 3

(2) _____ The following determinant evaluates to 0 .

− 1

(3) _____ The following determinant evaluates to 1 .

− 3

+ 2

− 2

− 1

(4) _____ The following determinant evaluates to 0 .

− 7

− 1

− 7

− 1

(5) _____ The following determinant evaluates to 0 .

− 6

− 5

(6) _____ The following determinant evaluates to 0 .

− 1

(7) _____ The following determinant evaluates to a ² − b ² .

− a

− b

− a

(8) _____ The following determinant evaluates to 1 .

− 3

+ 2

− 2

− 1

(9) _____ The following determinant evaluates to − 33 .

− 1

− 6

− 2

− 0

− 5

− 1

− 3

− 7

(10) _____ The following determinant evaluates to − 248 .

− 2

− 8

− 3

− 5

− 6

− 4

− 6

− 9

For (11) - (15) : Choose from (a) , (b) , (c) , (d) or (e) to select your answer to the problem.

(11) What value of x will make the following matrix determinant true?

− 12

− x

−

− 2

− 3

(a) − 18 (b) 12 (c) 42 (d) 24 (e) 16

(12) What value of x will make the following matrix determinant true?

− 7

+ 5

−

− 3

− x

− 9

(a) − 12 (b) 12 (c) 42 (d) 24 (e) 16

(13) 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

− 1

− 2

− 0

(a) x = 9 ; y = − 2 (b) x = 1 ; y = − 5

(14) What is the solution of this 2 by 2 system of equations, represented in matrix form?

+ 1

− 08

− 0

− 2

+ 2

− 24

− 0

(a) x = 10 ; y = − 2 (b) x = 10 ; y = 2

(15) 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

− 08

− 0

− 2

+ 2

− 2

− 16

− 0

+ 3

+ 5

− 1

+ 32

− 0

(a) x = 10 ; y = 1 ; z = − 2 (b) x = 10 ; y = 0 ; z = − 2

For problems (16) through (25) , refer to the ( x , y , z ) augmented matrix given below.

+ 1

− 1

+ 3

− 0

− 2

+ 2

− 1

− 4

− 0

+ 3

+ 5

− 3

+ 9

− 0

(16) This is a three row and four column augmented matrix. (a) True (b) False

(17) This is a four row and three column augmented matrix. (a) True (b) False

(18) The top row of the matrix represents the equation: x + y − z = 3 (a) True (b) False

(19) The last row of the matrix denotes the equation: 3 x + 5 y − 3 z = 9 (a) True (b) False

(20) The augmented matrix is a 4 × 3 dimensional matrix. (a) True (b) False

(21) The solution of the underlying system is: x = 1 , y = 0 , z = 2 / 3 (a) True (b) False

(22) The solution of the underlying system is: x = 7 / 3 , y = 0 , z = − 2 / 3 (a) True (b) False

(23) The above system is in the matrix form A x = B . (a) True (b) False

(24) 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

(25) 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

Answers

QuickHelper

(10)

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

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