4. Let T: R - R be a linear transformation such that 2x1 32 32 3 -1 22 + T3 T 2 Find the standard matrix of T. 5. Compute 3A - 4B, AB and BA: 021 3 1 0 and B -2 0 1 3 2 1 A = 1 -4 1 1 4 0 6. Find the inverse of each matrix BEE 0 1 -2 4 -6 and 1 1 3 -5 3 -1 1
0 -1 5 6 -3 6 Let C = and D = 7 4 0 1 4 0 Find -6C+ 3D □□□| |□□□□| Undefined
Let A 2 3 4 - 1-6 -20 3 6 -9 5 3 -2 7 Find each of the following bases. Be sure to show work as needed. 1 Find a basis for the null space of A. b. Find a basis for the column space of A. c. Find a basis for the row space of A. d. Is [3 2 -4 3) in the row space of A? Explain your reasoning.
[ 4 6 -61 Let A = -3 -4 3 . Find a basis for the eigenspace corresponding to the eigenvalue X = -2. [ 5 6 -7]
Lac-C1) 1 E C3x3 [6] (1 i 2 2. Let C = 1 5 (a) Use Gaussian Elimination to calculate C. (b) Is the linear system Cu = d consistent for any d e Caxi? Justify your answer. [3]
In the figure, let C1 = 4 μF, C2 = 2 μF,
C3 = 5 μF and C4 = 2 μF. Find the equivalent
capacitance between a and b. (Give your answer in
decimal using micro F as unit)
C C2 1 4
Let B = {bį, b2} and C = {C1,C2} be bases for R², where b, -6--0--0--01 1 a. Find P BEC [16 b. If [x]c = -3 de=[13] , find [x]
Problem 2 [2 4 6 81 Let A 1 3 0 5; L1 1 6 3 a) Find a basis for the nullspace of A b) Find the basis for the rowspace of A c) Find the basis for the range of A that consists of column vectors of A d) For each column vector which is not a basis vector that you obtained in c), express it as a linear combination of the basis vectors for the range of...
C1= 5
C2= 6
C3= 10
GCD --> Greater Common Divisor
B1 a. Let x := 3C1 + 1 and let y := 5C2 + 1. Use the Euclidean algorithm to determine the GCD (x, y), and we denote this integer by g. b. Reverse the steps in this algorithm to find integers a and b with ax + by = g. c. Use this to find the inverse of x modulo y. If the inverse doesn't exist why not?...
Let A = {1, 2}, B = {3, 5, 6}, C = {1, 2, 3, 5, 7}, D = {4, 7, 9}, and U = {1, 2, 3, . . . , 9, 10}. 1. Find B ∪ C. 2. Find B ∩ C. 3. Find A ∪ B. 4. Find C ∩ D. 5. Find C'. 6. Find B'. 7. Is 4 ∈ C? 8. Is B ⊆ C? 9. Is A ⊆ C? 10. Are A and B...