QUESTION 3 B Let A=M³ (f) B be the matrix associated with the linear map f((x,y,z) = (x - 2y,y+z,0) relative to the bases B={u= (1,0,3); v= (0, 2, 1); w=(2,1,0) } and B'= {u'= (0,0,2) ;v '= (1,0, 3) ;w'= (1,2,1) } . Then the third column of A is: O A. 1/2 1/2 - 1/2 B. 2 ORG) 3
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- Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a matrix whose Nullspace is spanLet x(¹) (t) = -3t e 4e-3t, 0 x (²) (t) = [_5e-³]; x (³) (t) = -5e-3t, Are the vectors x(¹) (t), x(²) (t) and x(³) (t) linearly independent? choose ◆ If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0 -3t [8] = 0[*]+[-+* 0 [4e-3t -5e-3t -0[ + -5e-3t -35e-3t -5e-3t -35e-3tFind the matrix A of the linear transformation from R2 to R' given by 5 T 6 x1 + -1 x2. %3D -8 7 A =
- From the system x' = -x + 5y og y' = -y show that the vector function (top of picture) is a solution of the system only if (bottom of picture) is true.Verify that the vector X, is a particular solution of the given nonhomogeneous linear system. Xp For Xp *' - (²₂) × - (₁₁)¹; *, -(1)² + (-1) out ↓)× let; Xp 2 1 = X' et tet 5 6 = · ( ¹)e² + (-1¹)te², one has Xp' 2 1 (3²) × - (₁1) ² - (11)et. 5 6 P Since the above expressions ---Select--- ✪, Xp 1 = (-¹) tel le + 1 tet is a particular solution of the given system.Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) {(0, 4,0, 0, 2), (0, 1, 3, 1, 1), (0, 2, 0,0,0)}.