
*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)
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
1. Let A Idef g h i Given that det(A) 1, find det(B) where You should fully justify your answer 3 marks]
Compute A.(4.29×1015)⋅(1.94×10−4). B. 6.28×1013+7.30×1011. Express your answers to three digits.
[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...