Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73,...
(1 point) If a 4 x 4 matrix A with rows vi , V2 , V3 , and V4 has determinant det A = 8, 5v1 +9v4 then det 6v1 6V4
(1 point) If a 4 x 4 matrix A with rows V1, V2, V3, and V4 has determinant det A = 2, 4v1 +6v2 5v1 + 9v2 then det = 1
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
Problem 2. (a) Let A be a 4 x 4 matrix with characteristic polynomial p(t) = +-12+} Find the trace and determinant of A. 2 e: tr(4) and det(A) = 0 12: tr(A) = 0 and det(A) 2 3 2 T: tr(A) = 0 and det(A) 3 : None of the other answers 01 OW
2 invertible? C For which values of c is the matrix 8 O c 4 c =-4 Both of the above, i.e., c +4 Neither of the above, i.e., c +4. Suppose that the following row operations: interchange rows 1 and 3 multiply row 3 by 1/2 add -3 times row 1 to row 2 2 1 7 in this order, transform a matrix A into B = | 0 4-5 L0 0 3 What is the determinant of A?...
Problem 6. (10 points) Suppose that A is a matrix with seven columns and four rows. Suppose that the columns of A span R. Determine the number of vectors needed to form a basis for the nullspace of T. Justify your answer.
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the determinant is det(A) --- 45. Find the eigenvalues of A. (1 point) Suppose that the trace of a 2 x 2 matrix A is tr(A) smaller eigenvalue larger eigenvalue Note: You can earn partial credit on this problem Preview My Answers Submit Answers Section 6.1 Eigenvalues and Eigenvectors: Problem 8 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues di < 12...
(4 points) For the function f(x) = 2? + 3.1, simplify each expression as much as possible. 1. f(x + h) – f(),h40 2. f(w) – f(x) +w Note: You can earn partial credit on this problem HW08 Section 3.3: Problem 11 Previous Problem Problem List Next Problem (4 points) Given the function f(1) = 5x - 4. calculate the following values: f(a) = f(a+h) = f(a+h)-f(a)
4. Let A and B be 4 x 4 matrices. Suppose det A= 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-1)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. [2] and us 6. (6 points) Let vi...