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For Problems 1-7, determine whether the given set
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- B1.arrow_forwardProblem 6. Prove that the vectors v₁ = (1, 0, -1), U₂ = (1, 2, 1), V3 = (0, -3,2) form a basis for R³. Express each of the standard basis vectors, (1, 0, 0), (0, 1, 0), and (0,0,1) as a linear combination of v₁, U2, U3.arrow_forwardProblem #9: Given three linearly independent vectors V₁ = (-9,3,-9,9,-2), V2 = (-8, 10, 9, -3, 10), V3 = (-7,-9,-7, -7,0), in RS, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e, and e; then enter the values of i and j into the answer box below, separated with a comma. Problem #9:arrow_forward
- need correct answerarrow_forwardEx. 600. Given the 2x2 Matrix A 1 2 11 3 Determine B=A+A and C=A-A Answers: B(1,1),B(1,2),B(2,1),B(2,2),C(1,1),C(1,2),C(2,1),C(2,2) Ex. 610. Given the 2x2 Matrix A 4 1 5 3 Determine B=A*A Answers: B(1,1),B(1,2),B(2,1),B(2,2) ans:4 Ex. 615. Given the 2x2 Matrix A 43 15 Determine B=transpose(A). Answers: B(1,1),B(1,2),B(2,1), and B(2,2) ans:4arrow_forwardPlease provide me accurate solution with explanation because I want to understand this. Thank youarrow_forward
- Prob. 3 A matrix A € Rmxn can also be viewed as a vector, by stacking all its n columns into a single length-mn column. Let x € R™, y ≤ R" be two column vectors. Show that (xy, A) = x¹ Ay.arrow_forwardThis question is about a problem in the following book: Linear Algebra and Its Application 5th Edition David C. Lay + 2 others Publisher: PEARSON ISBN: 9780321982384 I solved problem 33 in section 1.3, and I'm not sure if my solution is a valid proof. Please let me know if my solution is correct or if the problem can be solved similarly. The problem is attached as a picture.arrow_forward3. Matrices and vectors a. Compute the following [2 marks] -5x² + 7y² + 2x² + 2xy +8xz - 6yz • -5x² + 7y² + 2z² + 2xy - 6xz+8yz · 5x² + 7y² + 2z² + 2xy +6xz-8yz • 5x² + 7y² + 2z² - 2xy - 6xz+8yz b. What's the inverse of (² (x y z) -5 1 -3 G+90- 1 7 4 -3 4 2 =? ? You should use the definition of inverse and check the conditions for each matrix in turn. [2 marks] 2 2/3 1/31 -1/3 1/3 (12) (-1/3 2/3)arrow_forward
- Suppose that {u, v, w} is a set of three vectors, each of which is a member of R³, that {u, v} is linearly independent, and that w = 2u + 4v. Suppose that A is the matrix whose columns are (from left to right) u, v, and w. Which of the following is an echelon form of A? Select one alternative: 1 00 O 0 2 0 0 0 4 1 0 -2] O 10 1 -4 0 0 0 1 O 0 0 2 1 4 000 1 0 0 O 0 -2 0 0 0arrow_forwardFind a vector that spans the kernel of the following matrix: [ 1 0 2 4 ][ 0 1 -3 -1 ][ 3 4 -6 8 ][ 0 -1 3 4 ]arrow_forwardcompute the indicated matrices B -Carrow_forward
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