Problem #1: Consider the matrices 4O 10 20 28 0 7 x = , y = ' w = 4 9 1 + h 8 7 5 For what value of his the set {x, y,W} linearly dependent? Submit Problem #1 for Grading Problem #1 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem # 2: Which of the following sets of vectors are independent? (i) (l,l,3), (3, 3,4), (4,4,0) (ii) (1,1, 3), (3, 3,4), (7,7,4) (iii) (1,1, 3), (3, 3,4), (ll,ll,6) (A) none of them (B) (ii) and (iii) only (C) (ii) only (D) (i) and (ii) only (E) (iii) only (F) (i) and (iii) only (G) all of them (H) (i) only Problem #2: Just Save Submit Problem #2 for Grading Problem # 3: Find the standard matrix A for the transformation T: R3 > R4 given by x1 + .762 + X3 x1 .X1 + 3x2 3.763 T .762 = ( ) x1 + 9x2 + 9X3 X3 .X1 + 27.}:2 27.763 (3) What is the size of A? (If A is m x n, then enter the values of m and in into the answer box below, in that order, separated with a comma) (b) Multiply all the entries in the last row of A' What value do you get? Problem: l:l Submit Problem #3 for Grading Problem #3 Attempt #1 Attempt #2 Attempt #3 YourAnswer: 3(a) 3(a) 3(a) 3(b) 3(b) 3(b) YourMark: 3(a) 3(a) 3(a) 3(1)) 3(b) 3(b) Problem # 4: For the linear transformatation T: R3 > R3, the images of the following three vectors are given: 1 2 1 6 1 3 T(0)=2,T(1)=2,T(1)=2 0 0 0 _4 _1 4 Find the standard matrix for the transformation. Enter your matrix by row, with entries separated by commas. a b c Pmb'em #4: l:l e.g., [:1 e f:| would be entered as a,b,c,d,e,f,g,h,i. ghi Submit Problem #4 for Grading Problem #5: Let Mbe a 3 x 3 matrix. You are given that 4 4 Mn: 2 , Mv= 2 5 1 Consider the following statements. 4 (i) M(3u2v) = 2 13 4 7 (ii) M(%v) = 31 1 7 12 (iii) M(3u) = 6 15 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 '12,? into the answer box below (without the quotes). l Just Save l l Submit Problem #5 for Grading Problem #5 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #6: Consider the matrices 2 3 5 29 M = 3 5 2 , b = 23 3 7 6 33 Which of the following is such that M x = b? 6 3 3 1 (A)x= O (B)x = 1 (C)x = 0 (D)x = 1 14 7 7 3 Problem #6: l Just Save l l Submit Problem #6 for Grading T: 12 3 - R2 3 + [ : ] = + [ : ] - + [ : ]T: 12 3 - R2 3 + [ : ] = + [ : ] - + [ : ][ = ] = - [ 8 ] + ( 8 ] + () [;] L 3 0 D we have now transformation matrin is + [ !0. 0 ] T LOIOJ T [0 0 1 ] [100 ] - 2 4 3 [olo ] 2 O O 0 [OOD]L O Answer - 2 1 4 1 3 2 0 0 0 1 141 , 0