- A_nxn (square). Can Ax=0 have only the trivial solution?

a) No that statement is impossible

b) Yes when the columns of A are l.i. but we can't say anything more

c) Yes when the columns of A are l.i. and A has n pivot rows

d) Yes when the columns of A are l.i. and A has n pivot columns

e) Both c and d

- A_mxn (not square). Can Ax=0 have only the trivial solution?

a) No that statement is impossible

b) Yes when the columns of A are l.i. but we can't say anything more

c) Yes when the columns of A are l.i. and A has m pivot rows

d) Yes when the columns of A are l.i. and A has n pivot columns

e) Both c and d

- For the Hill Cipher

a) A_{nxn}[original message]_{nxp}=[coded message]_{nxp}

b) to decode, we must use apply an invertible matrix to the coded message and read the message along the rows

c) the method is vulnerable to those that intercept enough coded/decoded vector correspondances because of its linearity

d) all of the above

e) more than one of a), b) or c), but not all

- If the condition number of a square matrix with fractional entries
is 3.5 10
^{6}then

a) We should use 8 decimal places in our measurements of b if we want solutions to Ax=b to be accurate to 2 decimal places

b) The matrix is invertible

c) both of the above

d) none of the above

- The equation Ax=b has at least one solution for each b in R^n whenever A is an nxn matrix.

a) true

b) false and I can think of a counterexample

c) false and I can think of a correction

d) both b) and c)

e) other

- If there is a b in R^n such that the equation Ax=b is consistent, where A is nxn, then the solution is unique.

a) true

b) false and I can think of a counterexample

c) false and I can think of a correction

d) both b) and c)

e) other

1. e)

2. d)

3. e) (a and c--b should say columns)

4. c)

5. d)

6. d)