-4 6 6 5 0 Let A -17 4 4 B 1 3 1 -6 0...

Question

Question

-4 6 6 5 0 Let A -17 4 4 B 1 3 1 -6 0 -6 0 0 DC- 8 0 0 8 0 1 10 0 0 4 AB BC Prove WITHOUT using the product property of deter

Answer 1

Answer #1

geren So] - V ) -4 -) 3 0 6 = 9 0 - 1 4 -A -6 -6 o 0 :. AB: 1-5 -4 - 1 6 - 3 JI 0 4 0 -6 6 o 6 -4 0 O -30 q w 0 - 6 -12 0 o -

Answer 2

Similar Homework Help Questions

4. Consider R2x2 with inner product (A, B) tr(ATB), and let V CR2x2 be the subspace...

4. Consider R2x2 with inner product (A, B) tr(ATB), and let V CR2x2 be the subspace 1 1 1 0 This is consisting of upper-triangular matrices. Let B= a basis for V. (You do not need to prove this.) (a) (8 points) Use the Gram-Schmidt procedure on 3 to find an orthonormal basis for V. Find projy (B) (b) (4 points) Let B= 4. Consider R2x2 with inner product (A, B) tr(ATB), and let V CR2x2 be the subspace 1...
7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8...

7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8 3.1), of order n. Then, the product AB is also a lower triangular matrix. Likewise for upper triangular matrices. (We say that the set of lower triangular matrices, of order n, is closed under multiplication.) Prove this theorem, for n = 3, by multiplying the following two matri- ces: a1 0 0 A bi b 0 1 0 0 and B 2 0 21...
linear algebra Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and...

linear algebra Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and (a) Prove: V is a basis. (b) Find the coordinates of (b, b2, bs) with respect to V = {71, U2, 3,}. (c) Suppose M and M' are matrices whose columns span the same vector space V. Let b be the coordinates of relative to M. Write a matrix equation that gives b', the coordinates of relative to M'. (Your answer should be a...

mixture 3. Let 0 0 1 0 1 2 1 2 Z loo 4 X 0...

mixture 3. Let 0 0 1 0 1 2 1 2 Z loo 4 X 0 A= and B = Y 4 1 (a) Compute the determinants of the following matrices: A, B, AB, 5AB, and (AB) (b) Compute the inverse of A. X = 3 Y = 3 Z = 6
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6...

HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6 -2 1 a. (4 pts) Find the multipliers l21, 131,132 and the elemention matrices E21, E31, E32 b. (2 pts) Use the multipliers l21, 131,132 to construct the lower triangular matrix, L c. (2 pts) Use the elimination matrices to determine the upper triangular, U, matrix of A d. (2 pts) verify that LU A
Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve fo...

Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...

# 2 and # 3 2 -6 4 -4 0 -4 6 1. Define A =...

# 2 and # 3 2 -6 4 -4 0 -4 6 1. Define A = 8 01 . Determine, by hand, the LU factorization, of A. You may of course check your answer using appropriate technology tools. Then use your result to solve the system of equations Ax b, where b--4 2 0 5 2 2. Suppose A-6 -3 133Even though A is not square, it has an LU factorization A LU, 4 9 16 17 where L and...
[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without multiplying the matrices, 0 -1 1110 0 0 0 (a) Find the dimension of...

[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without multiplying the matrices, 0 -1 1110 0 0 0 (a) Find the dimension of each of the four fundamental subspaces. b have a solution? (b) For what column vector b (b, b2, ba)' does the system AX (c) Find a basis for N(A) and for N(AT). [1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without...
HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the...

HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the elementary matrices that perform the following row operations in sequence: a. 21 * 2 2. E31 : R3 R1R3 b. (3 pts) Show that the elementary matrices you found in (a) can be used as elimination matrices to determine the upper triangular, U, matrix of A. (4 pts) Find the lower triangular, L, matrix that verifies A C. = LU.

Let A and B be square matrices of order 3 such that |A| = 4 and...

Let A and B be square matrices of order 3 such that |A| = 4 and |B| = 7 (1) Find |AB|. (2) Find |2A|. (3) Are A and B singular or nonsingular? Explain. (A) A and B are both singular because they both have nonzero determinants. (B) A and B are both nonsingular because they both have nonzero determinants. (C) A is singular, but B is nonsingular because |A| < |B|. (D) B is singular, but A is nonsingular...