linear algebra 1. Let A be a square matrix with characteristic polynomial 13 – 912 +...
Elementary Linear Algebra 1. Let A be a square matrix such that detal - A) = 112 - 6211 +9210 a.) (3 points) What is the size of A? b.) (4 points) Is A invertible? Why or why not? c.) (3 points) How many eigenspaces does A have?
Help on this question of Linear Algebra, thanks. Let A be a square matrix. Prove that A is invertible if and only if det(A) +0.
1. Let A be a square matrix such that detal - A) = 112 - 6/11 + 9210 a.) (3 points) What is the size of A? b.) (4 points) Is A invertible? Why or why not? c.) (3 points) How many eigenspaces does A have?
Let A be a square matrix such that det(al – A) = 212 – 6211 + 9210. What is the size of A? Is A invertible? Why or why not? How many eigenspaces does A have?
Need Help ASAP!!!! Subject: Linear Algebra (a) Let A= r 7 T 5 2 4 0 1 i. Compute det A in terms of r. ii. Find all value(s) of z such that A is NOT invertible. (b) Let the characteristic polynomial of a matrix B be – 23 +22 +6%. i. Find the size of B. ii. Find all the eigenvalues of B including multiplicity. iii. Find the determinant of B.
Let A be an n × n matrix with characteristic polynomial f(t)=(−1)nt n + an−1t n−1 + ··· + a1t + a0. (a) Prove that A is invertible if and only if a0 = 0. (b) Prove that if A is invertible, then A−1 = (−1/a0)[(−1)nAn−1 + an−1An−2 + ··· + a1In]. 324 Chap. 5 Diagonalization (c) Use (b) to compute A−1 for A = ⎛ ⎝ 12 1 02 3 0 0 −1 ⎞ ⎠ . #18 a, b...
Let A be a square matrix such that detal - A) = 212 – 6211 + 9210 ..) (3 points) What is the size of A? .) (4 points) Is A invertible? Why or why not? --) (3 points) How many eigenspaces does A have?
linear algebra 1 2. Let A be the 3 x 3 matrix: A= 3 3 0 -4 1-3 5 1 (a) Find det(A) by hand. (b) What can you say about the solution(s) to the linear system Az = ? A. No Solutions B. Unique Solution C. Infinitely Many Solutions (c) Is A invertible?
Let A be a square matrix such that det(AI – A) = 212 – 6211 + 9210 (3 points) What is the size of A? (4 points) Is A invertible? Why or why not? I (3 points) How many eigenspaces does A have?
LINEAR ALGEBRA What are the eigenvalues of the matrix 2-31 1 -2 1 What is the characteristic polynomial of this matrix? (That is, the polynomial you use to find the eigenvalues). 1-32 p() = -13 +212 -1. op() = X(4-1)(-2) op() = 12 + 1 OPW) = 12 -2X + 1. Let M = 2-31 1 -2 1 1-32 (this is the same as the previous problem). Find the eigenvalues of M (they are not listed according to multiplicity). Let...