Matrix Operations

Which of the following matrix operations are defined? (Select all that apply)

• AB

• BA

• CD

• DE

• DF

Which of the following matrix operations are defined? (Select all that apply)

• $BA-ED$
  

• $B-CE$
  

• $B^2-EC$
  

• $AF-BE$
  

• $FA-EB$
  

Which of the following matrix operations are defined? (Select all that apply)

• $A^3$
  

• $B^3$
  

• $EC^2$
  

• $\left(EC\right)^2$
  

• $\left(CE\right)^4$
  

Which of the following matrix operations are defined? (Select all that apply)

• $BED$
  

• $BAD$
  

• $DAB$
  

• $BE^2$
  

• $CAF\left(E^T\right)$
  

 $A$   and  $B$  are square matrices such that  $AB=BA=I$  ​, where  $I$  ​ is the identity matrix.
Which one of the following statements is true?

•  $A^2=B^2$  

•  $B$   is not the inverse of  $A$  

•  $B$   must equal $A$  

•  $ABBABABBA=I$  

•  $ABBA+ABBA\ =\ 2I$  

• p=4, q=-2

• p=-2, q=4

• p=2, q=-4

• p=-4, q=2

Write the following simultaneous linear equations as matrix form:

3x – 2y = 5

9x + y = 1

Hence, using matrix method, calculate the value of x and y.

• x=1/3, y=-3

• x=1/2, y=-2

• x=-1/3, y=2

• x=1/3, y=-2

Which set of simultaneous equations is generated by the matrix equation above?

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Tags

CCSS.HSA.REI.C.8

 $5x+6y\ =\ 8$  

 $kx+3y\ =\ 5$  

For what value of  $k$  does the set of simultaneous linear equations above not have a solution?

 $kx-9y\ =\ 6$  

 $-3x+3y\ =\ -2$  

For what value of  $k$  does the set of simultaneous linear equations above have no unique solution?