In problem 15–18 use the method of Example 2 to compute eAt for the coefficient matrix. Use (1) to find the general solution of the given system.
16.
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- 4. Solve by Matrix Inversion. * For this number, solve using X = (A-1)B 2w – 2x + 3y + 4z = 33 3w – 5x – 7y + 3z = 11 4w + 3x – 4y – 5z = 3 5w + 4x + 6y – 2z = 45 1 Add filearrow_forward7. (S.15). Find the inverse A-1 of the matrix -2 -3 A = 0 2 -1 -1 -2 3arrow_forward2. Solve for x in the given matrix equalitiesarrow_forward
- 5. Given the matrix A=[²1] (a) Find the value of x that makes A singular. (b) Find the value of x that makes A-1 = A (i.e, that makes the matrix equal to its own inverse).arrow_forward5. Solve the system by using the matrix exponential 0 1 *=[ ¦ ¦] -+[2] » ²»-[:] x (1) -3t -2 3 0arrow_forwardQ5. Solve the following matrix equation. 19 [x} +5 [X]- 7. %3D -42 16 [0 =arrow_forward
- F28.arrow_forwardI need detail solution to help understandarrow_forward1. 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_forward
- 7. Let A be a matrix with a row consisting of all zeroes. If B is a matrix such that AB is defined, which of the following is always true? 8. Given the matrix B = 1 1 11 Which of the following (233) (a) 3 2 3 332 matrices solves X in the matrix equation X+13= 2(X - B)? (211) (d) 1 2 1 112 (322) (b) 2 3 2 2 2 3 (122) (c) 2 1 2 2 2 1arrow_forwardForm a coefficient matrix for the following linear system of equations: √x + 16 y = = 11 U x + 2y = -1. [26 11] 1 -1 [161] [11] Hi 0 [1¹9]arrow_forward2. (a) Find the condition number of the coefficient matrix in the system X1 (1461) (²2) = (2²6) X2 as a function of d > 0. (b) Find the error magnification factor for the approximate root xa = (-1,3+6).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning