a. Write down the matrix of coefficients and the

augmented matrix, and put both into echelon form.

Which statement is true about the rank of the two

matrices?

The rank of both matrices is always 2,

independent of the values of a and b.

The rank of both matrices is always 1,

independent of the values of a and b.

The rank of one matrix depends on the values

of a and/or b, but the rank of the other matrix

does not.

The ranks of both matrices depend on the

values of a and/or b./nb. Match the graphs to the cases:

No

solutions

1.

-4

-3

Infinitely many

solutions

-2 -1

4-

2

0

-2-

1/nc. For what value(s) of a can we have no solution to the

system of equations?

a =

ab

sin (a)

ә

əx

f

8

R/nd.

Reminder: check the formatting instructions

above.

For what values of a and b do we have infinitely many

solutions?

Give your answer as the pair of coordinates (a, b).

(a, b) =

ab

sin (a)

018

f

8

8/ne. In the case(s) where the choices of a and b mean

there are infinitely many solutions, the variables x and

y are related by an equation. Rearrange the equation

to find the formula for y in terms of x

y =

ab

sin (a)

Ә

f

əx

8

α/nf.

Reminder: check the formatting instructions

above.

Finally, in the case where there is exactly one solution,

find the formulas for x and y in terms of a and b.

x =

b

sin (a)

Ə

əx

8

8