4. Let H be the 4 x 4 matrix of all ones. Use three different values...
(1 point) Perform one step of row reduction, in order to calculate the values for x and y by back substitution. Then calculate the values for x and y. Also calculate the determinant of the original matrix. (Note: since the determinant is unchanged by type 3 row operations, it will be easier to calculate the determinant of the row reduced matrix.) (12 32] [31 = [1] det =
(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) =
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 12 Let B be the matrix given by A= 4 0 b b (a + b) 26 a a where a and b are indeterminates. a) (6 pts] Using row operations that exist for all values of a or b, together with cofactor expansion, compute the determinant of A expressed as a function of a and b. b) (4 pts] Use this to determine a relation between a and b that provides necessary and sufficient conditions for the matrix...
Review 4: question 1 Let A be an n x n matrix. Which of the below is not true? A. A scalar 2 is an eigenvalue of A if and only if (A - 11) is not invertible. B. A non-zero vector x is an eigenvector corresponding to an eigenvalue if and only if x is a solution of the matrix equation (A-11)x= 0. C. To find all eigenvalues of A, we solve the characteristic equation det(A-2) = 0. D)....
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations) Question (7) Consider...
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
1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can be computed by a cofactor expansion across the ith row of A, that is, det A H-1)adtAj Hint: Use induction on i, For the induction step from i to i+1, flip rows i and i+1 (How does this change the determinant?) and use the induction assumption. 1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can...
1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula 0 0 1 -3 -x X Question 4: (2 points) a b c fis 3, find the determinant of these matrices: If the determinant of the matrix M = d e (gh k) b a C (a) 7 d 7e 7f h k -E. b-2 e c - 2 f a...