Matrices

Question 1

diagonal matrix

Answer 1

• square matrix

- all the non-diagonal entries are zero

Question 2

scalar matrix

Answer 2

diagonal matrix with leading diags all the same #

i. e
- square
- all non diag entries 0
- all diag entries same #

Question 3

identity matrix

Answer 3

if scalars in scalar matrix are all 1’s

i. e
- square
- all non diag entries 0
- all diag entries are 1

Question 4

rule for maultiplying 2 matirces A and B

Answer 4

cols in A = #rows in B

Question 5

what is the span of a set of matrices

Answer 5

the set of all linear combinations of the matrices

Question 6

when are two matrices of the same size linearly independent

Answer 6

when the only solution tothe linear comnination is the trivial solution , i.e. c1 = c2 = c3 = 0.

if non-trivial soln then thes matrices are linearly dependent

Question 7

transpose rules:

1. (AT) T
2. (A + B)T
3. (kA)T
4. (AB)T
5. (A^r)T (wherer must be a positive integer)

Answer 7

1. (AT) T = A
2. (A + B)T = AT + BT
3. (kA)T = kAT
4. (AB)T = BT AT (ORDER!!)
5. (A^r)T = (AT)^r (wherer must be a positive integer)

Question 8

why is gaussian or gauss jordan elimination faster than inverse method for solving systems of linear equations

Answer 8

the inverse method works only if matrices are

• square
• invertible