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3 points

How Did I Do?

What is the rank r of the matrix

-2-2-1

11-2

-4-4-5 ?

000

00-2,

T=

aº

sin (a)

16

a

8

a

Ω/nQuestion 3

16 points

How Did I Do?

Format:

If you have more than one answer to a question, enter your answers separated by a comma

. I no solution exists, enter the single character

(without the quale marks

Give your answers in exact form (ie do not use decimal approximations

Use to explicitly indicate multiplication between variables and other variables, between variables and brackets, or between sets of

brackets (eg. x'y rather than xy, 2(x+y) rather than 2(x+y)

Here is a system of two linear equations with two unknown constants and b

-2

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.

b. Match the graphs to the cases:

.. No solutions

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/orb.

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Infinitely many solutions

6-a-y+16-2-7

25-a-z+6-y-4-3

0

Exactly one solution

3/n3/nShow/hide

e. For what vake(s) of a can we have no solution to the system of equations?

Gm

asin (a)

Reminder check the formating instructions above

00 a

In the case whe

equation Range the equ

-3-

(a)

(2

For what values of and do we have intritely many solutions?

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

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3

nly mary solutions, the variables and are related by an

of

3/nReminder check the formating instructions above

Finely in the case where there is exactly one solution, find the formule forze and g in terms of and

08:

DC G D

3

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5