In Problems 1–6 write the given linear system in matrix form.
6.
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Differential Equations with Boundary-Value Problems (MindTap Course List)
- 16. Assume x E R. Give the matrix associated with the quadratic form 3(x,)? + 4(x2)2 – 2x,x2 + 3x1X3 – X,X3. |arrow_forward9. P = 15 -4 -7 2e31 – 8e- -4e31 + 2e- ž(1) = | 3e3t – 20e- -6e31 + 5et Show that x1 (t) is a solution to the system x = Px by evaluating derivatives and the matrix product -4 ž(1) = | 15 -7 Enter your answers in terms of the variable t. Show that x2(t) is a solution to the system x' = Px by evaluating derivatives and the matrix product 9. 3(1) = | 15 -4 X2(t) -7 Enter your answers in terms of the variable t.arrow_forwardWrite the given linear system without the use of matrices. (1)-(1)-·-(-)) -t + 2 e 2 X d - D y. dt 1 Z 8 dx dt dy dt dz dt || = )-(-3 1 -1 9 X -6 -2 5 y 3arrow_forward
- 1. Find the general solution of x1 =x2 – x1 + t, x, =x2. (1 2 3 4 5 6 2. Explain why we cannot aclculate the matrix product AB, where A = and B 1 2 -3 4 5 -6arrow_forward3. Illustrate the Gersgorin theorem by the matrix 1 2 | 1+ 2i A = -1 1 -2 – 2i - -Narrow_forward8. Solve the given (matrix) linear system: X' = ; *+(*) (3cos(t) 14 2 2etarrow_forward
- The matrix that projects onto the line y = -x is X 0.6 0.8 0.8 -0.6arrow_forward2. Write the following functions in matrix form: (a) f(x1,x2, x3) = (x1 + 2x3, x1 + 3x2 – 23, X1) (b) f(x, y, z) = 3.x2 + 2y2 – 4z2 + xy – 4zy +xz (c) f(r, s,t) = 2r² + 3s² + 4ť² – rs + 5rtarrow_forward4. Find the standard matrix for T where T(a) (2x,+x 1-2x2).arrow_forward
- 5. Find the cofactors and the adjoint matrix of A where (1 1 -1 b) A =| 2 3 (7 0 -1 a) A = - 2 0 - 2 4 -3 5 4 5 6 2arrow_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_forwardHomogeneous Systems In Problems 53–55, determine all the solutions of Ax = 0, where the matrix shown is the RREF of the augmented matrix (A | b). ri -2 0 5 0 1 2 0 0 0 53. 0 lo 1 55. (1 - 4 3 010]arrow_forward
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