1. Find the determinant of the follow ing matrices 1 8 [2 1 B=3 8 10...
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
If A and B are 3x3 matrices and A = 1, |B 3, compute the determinant If A and B are 3x3 matrices and A = 1, |B 3, compute the determinant
(1 point) Find the determinant of the matrix A= -9 1-8 3 | det(A) =
8. Find the determinant of the following matrices using a minimal cofactor expansion. Do not manipulate the rows A=0 0 0 31 2 5 -3 0 - 9. Determine for what values of s, the following system has solutions for. Use Cramer's rule to determine what the solutions would look like in terms of s 3sx +y = 6 100x + 12sy = -8 10. (a) Use a determinant to find the area of the parallelogram S with vertices at...
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-A-t +1 where t = Tr(A). 44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove...
1. (10 points) Let A and B be 3 x 3 matrices, with det A = -3 and det B = 2. Compute (a) det AB (6) det B4 (c) det 3B (d) det A"B" AT (e) det B-AB
1. Let A and B be two 4 by 4 matrices with (let A =-2 and det B-1-8. Find det(-2.1' B) 2. Assume that A is a 4 x 4 matrix and det (Adj(A))-8, find det(A) 3. Find the inverse the given matrice by way of elementary row operations
: [3 marks] Let A and B be 3 x 3 matrices. Consider the following statements. (1) If det(A) = 1 then det(24-1) = 2 (11) det(I + A) 3+det() (111) det(A + BT) = det(B+ 4) = Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True False False, then you would enter '1.2.2' into the answer box below (without the quotes).
Exercise 6.4.2. (5 points) Use Gaussian elimination to compute the determinant of the follow- ing matrix: 1 1 2 1 2 -1 2 0 4 1 1 -1 5 2 3 ܒܬ ܒܝܪ
2. In what follows, A, B denote two square matrices. Prove the follow- ing statements using the appropriate definitions. (a) If v is a common eigenvector to A and B, then v is also an eigen- vector of AB (b) If A is diagonalizable and B is similar to A, then B is also diago- nalizable.