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C WeBWorK assignment due : 02/19/2021 at 11:59pm EST. 1. (1 point) If 

−1  −5  A= 0 0

then

−1 −4 0 0

0 0 1 3

(ii) Find the solutions to the two systems by using the inverse, −1 i.e. by evaluating  hand side  A B where B representsthe right  −3 1 for system for system (a) and B = (i.e. B = −4 −1 (b)). Solution to system (a): x = ,y= Solution to system (b): x = ,y=

 0 0  , −1  −4



5. (3 points) In each part, find the matrix X solving the given equation.       8 5 10 0 . X= X= a. 0 1  −3 6     5 −4 0 1 . X= X= b. 1 0    10 1    5 −3 1 9 . X = X= c. −9 9 0 1       −1 −4 1 −1 . X= X= d. 7 2 −1  7   4 1 6 1 0 0 −6 5 . e.  0 1 0  X =  7 0 0 9  −10 5 1 



 A−1 =  

 . 

2. (1 point) Write the system of linear equations   8x + 8y − 9z = −5 −9x + 4y + 4z = −3  −8x + 3y − 5z = −4

as a matrix equation.



  x  y =  z

 



X=





0 0 f.  0 1 1 0 

3. (1 point) If A= then A−1 =





−9 −6 −6 5



,

X=

 . 



1 g.  0 0 

 −1 , solve A~x = ~b. −2

Given ~b =   ~x = .

X=

4. (1 point) Consider the following two systems. (a) 

−6x + 2y 2x − 3y

= =



−6x + 2y 2x − 3y

= −3 = −4



 −8 9 9 −7  . 1 5

  0 1 −2 0 X = 8 5 1 − 3 8 

 7 −5  . −6



A=



A=



7. (1 point) Enter a 3 × 3 skew-symmetric matrix A that has entries a12 = 2, a13 = 5, and a32 = 1.  

(i) Find the inverse of the (common) coefficient matrix of the two systems. 

  4 1 0 X =  5 0 9

6. (1 point) Enter a 3 × 3 symmetric matrix A that has entries a11 = 2, a22 = 0, a33 = 4, a12 = 1, a31 = 5, and a23 = 3.  

1 −1

(b)

A−1 =

0 1 10





Generated by WeBWorK, c http://webwork.maa.org, Mathematical Association of America

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