Question

@watchmath can you help me with this as well?

Answer 1

jal

Answer 2

?

Answer 3

is this correct? what do i do next?

Answer 4

1 8 a
-3 -8a -9
a 24 9

Get rid of -3 in row 2 by multiplying first row by 3 and adding it to second row

Get rid of a in row 3 by multiplying first row by -a and adding it to third row

1 8 a
0 24-8a 3a-9
0 24-8a 9-a^2

Eliminate (24-8a) in third row by subtratcing third row from the second row

1 8 a
0 24-8a 3a-9
0 0 a^2 + 3a - 18

When will the third row be all zeros?
When a^2 + 3a - 18 = 0
(a + 6)(a - 3) = 0
a = 3 or a = -6

If a = 3, the matrix is:

1 8 3
0 0 0
0 0 0 So the rank = 1 when a = 3

If a = -6, the matrix is:

1 8 -6
0 72 -27
0 0 0 So the rank = 2 when a = -6

For all other values of a, the rank will be 3

Answer 5

thanks