4. Use row operations to show that det X y y² 2² Z = (z − x)(z − y) (y – x).

5. a) Make tables of values for y = x², y = 2x², y = x² + 1, and y = (x – 3)². b) Compare the y-values for y = x² and y = 2x². c) Compare the y-values for y = x² and y = x² + 1. d) Compare the y-values for y = x² and y = (x – 3)².

1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.

Find b and c so that y = − 13x² + bx + c has vertex (4, −4). b= C =