*3.2.29 1011 Compute det B4 where B = 2 2 4 (132 det B4 = (Simplify...
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
Question 2. Let 1 -15 B = 1 1 2 V2 a) Compute B2, B3, B4, B7, and B8. b) Use part a) to determine B2020. Show your work. c) The matrix B is invertible. Use part a) to find B-1. Justify your answer. (Note: no marks will be given if either the formula for the inverse of a 2 x 2 matrix or row reduction is used to compute B-1)
1. Let A Idef g h i Given that det(A) 1, find det(B) where You should fully justify your answer 3 marks]
Linear Algebra:Question 5 [10 points] If A, B, and C are 4×4 matrices; and det(A) = 4, det(B) = −5, and det(C) = −4 then compute: Question 5 [10 points] If A, B, and C are 4x4 matrices; and det(A) = 4, det(B) = -5, and det(C)=-4 then compute: det(2CT A-18-10-1BICI) = 0
[4 points Suppose A, B, and Care 5 x 5 matrices with det(A) = -2, det(B) = 10 and the columns of C are linearly dependent. Find the following or state that there is not enough information: (a) det(10B-) (b) det(AB) (c) det(CA+CB)
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...
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...
If A and B are 3 x 3 matricies for which det A = 2, det B =-2 find the following determinants: (all entries below are either integers or proper fractions in lowest terms) det(A)- det(B-44BA) = det(4(A(B-1)) detC4BT)-1) =
2 Lots - Ja 67 (a) Show that X(X) = 12 - T(A)+det(A), where TY(A) = a + d is called the trace of A. (b) Show that the eigenvalues of A are [(a + d) + V (a – d)2 + 4bc] 11 007 3. Let A = 1 2 3 (a) Compute x1(4). (b) Compute the eigenvalues of A (c) Compute the matrix A-4A? - 7A+101. (If you find this phenomenon interesting, google the "Cayley-Hamilton Theorem”.) Command command...
2 Applied 2 -3 -10 2 If A = and B- compute AB and BA, if possible. -3-5 2 4 - 4 2 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. GES A. AB - (Simplify your answers.) B. This matrix operation is not possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. E02 abra OA. BA- (Simplify your answers.) B....