Let A, P, and D by n x n matrices. Mark each statement true or false. Justify each answer.
a. A is diagonalizable if A = PDP^-1 for some matrix D and some invertible matrix P. Choose the correct answer below.
O The statement is true because the columns of P are the n linearly independent eigenvectors of A.
O The statement is false because A must have n distinct eigenvalues for the matrix D and P to exist.
O The statement is true because if A = PDP^-1, then A is diagonalizable by definition.
O The statement is false because the symbol D does not automatically denote a diagonal matrix.

For [tex]f(x) = 4x+1[/tex] and [tex]g(x) = x^{2} -5[/tex] find [tex](f[/tex] ° [tex]g)[/tex][tex](4)[/tex]

Which equation represents a line that is parallel to the line whose equation is 3x-2y=7( show all work)

Guys i need ! graded assignment grade 8 checkpoint 2, part 2 answer the questions below. when you are finished, submit this assignment to your teacher by the due date for full credit. total score: of 9 points (score for question 1: of 4 points) 1. the cost of renting a car for a day is $0.50 per mile plus a $15 flat fee. (a) write an equation to represent this relationship. let x be the number of miles driven and y be the total cost for the day. (b) what does the graph of this equation form on a coordinate plane? explain. (c) what is the slope and the y-intercept of the graph of the relationship? explain.