Problem # 1: Consider the matrices l6 3 l 32 O 8 x = , y = , w = 20 7 0 + I? 4 2 s For what value of I? is the set IX, 3', w: linearly dependent\".j Just Save 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) (3, 3, 3). {1, 2, 2], (2, 5, 5) (ii) {3. 3. 3}, (1, 2. 2), {1, 2, 2} (iii) (3, 3, 3), (1, 2, 2}, (3, 12, 12) {A} (i) and {iii} only (E) {ii} only (C) {ii} and (iii) only (D) none of them (E) (i) only (F) all of them (G) (i) and {ii} only (H) (iii) only Problem #2: Just Save Submit Problem #2 for Grading ' Problem #2' Attempt #1 ' Attempt #2 I Attempt #3 ' Problem #3: Find the standard matrix A for the transformation 1"": R3 > R4 given by X1".T2*.T5 x1 4.\\'13.Y2 \" 21'} T( *2 )= l6X1 9X2 4X3 X3 64.Y1 27X; 8X3 (a) What is the size of A? [If A is m X n, then enter the values of m and 1': 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? I Just Save I I Submit Problem #3 for Grading I Problem #3 Attempt #1 Attempt #2 Attempt #3 Your Answer: 3(a} 3(a} 3(a} 3(b) 3(b) 3(b) Your Mark: 3(a} 3(a} 3(a} 3(b) 3(b) 3(b) Problem #4: For the linear transforntatation T : R3 >R3. the images of the following three vectors are given: 1 0 l 4 1 8 T( 0 l: 5 .. T( l )= 5 . T( 1 )= 5 0 0 0 l 1 1 Find the standard matrix for the transformation. Enter your matrix by row, with entries separated by commas. -- - - I la l: Cl Problem #7: Determine the value of b that would guarantee that the below linear system is consistent. x1 - 2x2 - 6X3 = -6 2x1 - 4x2 - 613 = 2 -2x1 + 4x2 - 6x3 = b Problem #7: 20 Just Save Submit Problem #7 for Grading Problem #7 Attempt #1 Attempt #2 Attempt #3