A6 Suppose = A - Find an invertible matrix P and a diagonal matrix D so that A of P, a power of D, and P-¹ in that order. = 7 4 -8 -5 PDP-¹. Use your answer to find an expression for Aº in terms

Find the matrix of the quadratic form. Assume x is in R³. a. 2x² + 3x²2 - 9x²3 - 10x₁x×2 + 18x₁×3 − 12×2×3 b. 2x1x2 + 12x₁X3 - 18x2x3 a. The matrix of the quadratic form 2x² + 3x2 -9x3 - 10x₁x2 + 18x₁ x3 - 12x₂x3 is (Simplify your answer.) Part 1 of 2

Obtain the matrix sI-A

For this exercise assume that the matrices are all nxn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer. If the equation Ax = b has at least one solution for each b in R, then the solution is unique for each b. Choose the correct answer below. A. The statement is true. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R", then matrix A is invertible. If A is invertible, then according to the invertible matrix theorem the solution is unique for each b. OB. The statement is true, but only for x 0. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R, then the equation Ax = 0 does not only have the trivial solution. OC. The statement is false. By the…