In Problems 21–24 verify that the
21.
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- 4. (S.10). Use Gaussian elimination with backward substitution to solve the following linear system: 2.r1 + 12 – 13 = 5, 1 + 12 – 3r3 = -9, -I1 + 12 +2r3 = 9;arrow_forwardHello, I need help with this Linear Alegebra problem. Thank you!arrow_forward[1 1 1] 024. The system of equations | 0 0 1x=| b, | is solvable if |0 0 1 b, (c) b, = b, (d) b, = 0 (e) none (a) h, = b, = 0 (b) b, = b, # 0 025. If A = B+C and B= B' and C' =-C, then %3D %3D (1) C = A– A" »C=÷(4- A') (6) C=;(4+A") (4) C = A+ A" (e) none c=-(4-A') (0) C = (A+ A°) («)C= A+ A°arrow_forward
- 1. Find y by Cramer's rule for the following linear system. x+Oy+2z 6 -3x+4y+6z= 30 --2y+3z%=8 rallclenined with sides F(1,-3. -1).arrow_forwardHello, I need help with this Linear Alegebra problem. Thank you!arrow_forward,solve x′= Ax by determining n linearly independent solutions of the form x(t)=eAtv.arrow_forward
- 1. 2. 3. For which values of a and b is the following system of equations inconsistent. x+2y3z = 4 3x = y + 5z = 2 4x + y + az = b (a) a= 2 and b = 6; (d) a = 1 and b = 3; (d) A = Find the standard matrix for the operator on R² which contracts with factor 1/4, then reflects about the line y = x. 0 (a) A = 1/4 0 (₁/11) ( 0 1/4 1/4 ¹/4) 0 (b) a = 2 and b = 6; (e) None of these. (c) a 2 and b = 6; 0 1/4 - (¹/4) 0 (e) None of these (b) A = (e) None of these (c) A = The linear operator T : R³ → R³ is defined by T(x₁, x2, X3) = (W₁, W2, W3), where w₁ = 2x₁ + 4x2 + x3; W₂ = 9x2+2x3; W3 = 2x1 8x2 - 2x3. Which of the following is correct. (a) T is not one to one. (b) T is one to one but the standard matrix for T-¹ does not exist. (c) T is one to one and its standard matrix for T-¹ is (d) T is one to one and its standard matrix for T-¹ is HOLI 0 1 (88) 0 3 0 1 3 3 WIN - WIN 3 0 1 3 1 -4 3 -3 2 -3 1623arrow_forward2. Find the general solution of the following linear system: X + 3z = 1 Зх + у = 1 None O (-3t + 1, 6t + 1, t) O (-3t + 1, 9t – 2, t) O (i + 2, 1 – 1, t) | 6. (8 – 1, t – 5, t)arrow_forwardIn Exercises 11–14, find parametric equations for all least squares solutions of Ax = b, and confirm that all of the solutions have the same error vector. 1 3 1 12. A = -2 -6 |; b = ! 0 3 9. 1arrow_forward
- a) (2. 0. 1) b) (3. I. -I)/ 3 (0, 1. 0) d)(3, 7. 5) ) (18. 43. 30)S Q9. Let the vectors X1, Xz and x3 be the solutions to the systems Ax, = 0. Ax, = |1 and Ax, =0. lo %31 respectively. If A is invertible, then the second column of A-' is a) xi (b) x,) c) X3 d) (0. 1.0) (0 0 3 e) (1.1.1) ar the matrixarrow_forwardQ2. Find the basis and dimension of the solution space of the homogeneous linear system X1 – 4x2 + 3x3 – X4 = 0 2х, — 8х, + 6х; — 2х, —D 0 -2 2 3] Q3. Let, A =|-2 3 2. Find the eigenvalues and bases for the eigenspace of A and A-1. [-4 2 5arrow_forwardThis is the first part of a four-part problem. Let P = 2e3t – 6e -4e3t + 2e 1(t) = [3et 2(t) = -6e3t + 5e] 15et a. Show that j1(t) is a solution to the system i' = Pỹ by evaluating derivatives and the matrix product 9 = 15 Enter your answers in terms of the variable t. b. Show that ğa(t) is a solution to the system j' = Pj by evaluating derivatives and the matrix product = Enter your answers in terms of the variable t. 8 ]- [8 ]arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage