Say that A is a 3 x 3 matrix and that there are non-zero vectors x,...
8х — 2у + 3z. (3 points) Let x, y, z be (non-zero) vectors and suppose w = If z y-4x, then w = x+ -4 1 у. Using the calculation above, mark the statements below that must be true. A. Span(w, z) = Span(y, z) B.Span(x, z) Span(w, z) C. Span(x, y, z) = Span(w, x) |D. Span(w, y) = Span(w, y, z E. Span(x, z) Span(x, y)
6. True or False: (a) An eigenvalue of the matrix A is a non-zero vector y such that Ac = Xū. (b) Let A be a 3 x 4 matrix. Then ker A is non-trivial. (e) Let A be an n x n matrix. Ta is injective (i.e. one-to-one) if and only if TA is surjective (i.e. onto). (d) If A is a singular matrix, then A must have an eigenvalue. (e) The set {A € M,(F): det(A) = +1}...
12х + 18у — 4z. (1 point) Let x, y, z be (non-zero) vectors and suppose w = If z 2x 3y, then W = X+ у. Using the calculation above, mark the statements below that must be true. |A. Span(w, x) Span(w, z) B. Span(w, y) Span(w, y, z) |C. Spanx, y, z) = Span(x, y) D. Span(w, z) Span(x, y) E. Span(w, x, z) = Span(w, x, y)
Answer Save the vectors are any non-zero vectors Determine ir the following statements are True or False. Assume )M (b) The intersection of Z = (x2+4)cosy + 9xy and the plane, y-r, is a parabola. (c) The vectors 47- 97+20k and 87- 187-40k are parallel. (d) The graph of fix.) = x2 + r2 is a circle. (e) The spacing of the contours of a function of 2 variables given by y 3x2+C2 will increase as C increases. Answer Save...
Question 5 True of False part II: 5 problems, 2 points each. (6). Let w be the x-y plain of R3, then wlis any line that is orthogonal to w. (Select) (7). Let A be a 3 x 3 non-invertible matrix. If Ahas eigenvalues 1 and 2, then A is diagonalizable. Sele (8). If an x n matrix A is diagonalizable, then n eigenvectors of A form a basis of " [Select] (9). Letzbean x 1 vector. Then all matrices...
Let k be an integer such that the vectors and 3 are linearly dependent. What must be the value of - 1, 2 [1] [-1 Answer: 1 Incorrect. Try again Next page bus page 1 1 1] Let A = 1 -1 2 and x = 22 Lo -2 1] [3] [1] Let p = 2.9= 0 and r = 2 Lo] How many of the systems Az = p.Az =q, Az = r have at least one solution? (1)...
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if false what would make it true, or a counterexample - 2 pts each: a. If Spanv v, V}) = Span({w,W)= W , then W is 2-dimensional. b. The kernel of a linear transformation T: R8 -R5 cannot be trivial c. If A is an invertible matrix, then A is diagonalizable 0, then A cannot be full-rank d. If det(A) e. If A is an...
Suppose A is a 3 x 3 matrix that is nilpotent but not zero. So Ak-0 for some k 〉 1 A. Verify that 0 is an eigenvalue of A B. Verify that 0 is the only eigenvalue of A. C. Is it possible that there is an invertible matrix P such that P- AP is diagonal?
Let x, y, z be (non-zero) vectors and suppose w = -16x - 4y + 2z.If z = 4x + y, then w = - 8x - 2y.Using the calculation above, mark the statements below that must be true.
Let A be a 2 x 2 matrix with an eigenvalue equal to 1 and no other eigenvalues. Which of the following is necessarily true? a. A is symmetric. b. A is positive-definite. C. A is diagonalizable. d. A is invertible. e. Any of the above statements may be false.