• 

• Do the following. They will be referred to in class several times.
  

• Do Problem 1a,b,c.
  

• Do Problem 2 above.
• Do 3 (a,b,d)
  

• Do 4 (a)   –   Notes:
  • B² means BB,
  • B³ means B²B, etc.
  • AA^T means A times A^T.
  

• In problem 4, also determine A^TA.
  Does AA^T   =   A^TA?

• Given matrices:

  A   = 8   6 4   9

  and

  B   = 4 –19 –7 33

  Determine the products AB and BA. Are the two results equal?

• What is a matrix with only one column called?

• What is a matrix with only one row called?

• If A is non-square, does A² exist?

• What is (A^T)^T?

• Suppose A is 100 x 77.
  1. What is the size of A^TA?
  2. What is the size of AA^T?

• If A is a column vector containing n members, what is its size?

• If A is a row vector containing m members, what is its size?

• What is the transpose of a row vector?

• What is the transpose of a column vector?

• Which of the following is correct? When we write AB, we say that
  1. A pre-multiplies B.
  2. B pre-multiplies A.

• Which of the following is correct? When we write Ax, we say that
  1. x pre-multiplies A.
  2. x post-multiplies A.

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