Let the Number of Songs in the Music Player of Lou be : L
Given that Kelly has 4 times as many songs as Lou has in her Music Player
⇒ The Number of songs in Music Player of Kelly = 4 × L
Given that Tiffany has 6 times as many songs as Lou has in her Music Player
⇒ The Number of songs in Music Player of Tiffany = 6 × L
Given that Altogether have 682 songs in their Music Players
⇒ Tiffany songs + Lou songs + Kelly songs = 682
⇒ 6L + L + 4L = 682
⇒ 11L = 682
⇒ L = 62
⇒ Number of Songs in Music Player of Lou = 62
⇒ Number of Songs in Music Player of Kelly = 4 × L = 4 × 62 = 248
Since the maximum budget that Jennifer has is $62.10. You can input P=62.10 so now you can start solving.
Steps: 62.10 = (20+0.5x)+0.15(20+0.5x)
62.10 = 20 + 0.5x + 3 + 0.075x
(Combine "like" terms: so for here you combine x together)
62.10 = 0.575x + 20 +3
62.10 = 0.575x + 23
-23 - 23
39.10 = 0.575x
(Now divide 0.575 on both sides.)

You should end up with:
x = 68
Jennifer can have 68 pages in her book to fit her budget.
A, 4(750c - 700t). Hope this helps.
Answer:
I.
A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4
Null space is exactly two dimensional plane
dim null (A) = 2
II.
Rank A = dim U - dim Null A = 5 - 2 = 3
III.
Number of linearly Independent columns of A is the rank of A = 3
IV.
Yes, The system Ax = b has no solution sometimes as range of A \neq V
V.
Yes,Sometimes Ax = b has a unique solution
VI.
Yes, sometimes Ax = b has infinitely many solutions
The estimate of 3630 is 4000. because the hundreds place is higher than 5, so you would go a number higher