In Problems 1–6 write the given linear system in matrix form.
4.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 9. (a) Evaluate the matrix product Ax, where A = 1. and x = 3 Hence show that the system of linear equations 7x + 5y = 3 x + 3y = 2 can be written as Ax b where b = %3D (b) The system of equations 2r + 3y – 2z = 6 x– y + 2z = 3 4x + 2y + 5z = 1 can be expressed in the form Ax = b. Write down the matrices A, x and b.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_forwardProblem 8. Determine whether the 2×2 matrix (1) is in the span of {(18), (11),(18)}. 1arrow_forward
- 3. Q1: Given A = -1 4 3 3. find the matrix X if 2xT-AB = -2 B = 1 -3arrow_forwardHELP WITH 18 AND 19 In each of Problems 12–23, find AR and produce a matrix 2r such that QRA = AR. -1 4 2 3 -5 7 1 18. A = 1 -3 4 4 19. A = 0 0 0arrow_forward13 () 9. If A is a 3 x 3 matrix such that A 1 and A 4 1 then the product A 7 is %3D %3D 8arrow_forward
- Solving Systems Use Gauss-Jordan reduction to transform the augmented matrix of each system in Problems 24–36 to RREF. Use it to discuss the solutions of the system (i.e., no solutions, a unique solution, or infinitely many solutions). 74 + 25 - - 2 29. x₁ + 4x₂ = 5x3 = 0 2x1x2 + 8x3 = 9arrow_forward3. Let A be a 4 × 4 matrix. Suppose the matrix equation A = has solution set 1 what is the solution set of A = 0? 2.arrow_forward4. Solve the following system of linear equations with the inverse of the coefficient matrix (Solving for X from AX = B). x-2y+3z = 4 x+ y+ z = 2 (a) 2x + y+ z = 3 (b) x+3y+2z =1 5y-7z =-11 2x+ y- z = 2 x+2y+3z =1 4x+ y– z = 2 2x - y+4z = 3 3x+ y+ z =17 (b) (d) x+2y- z = 2 -x- 2y+ 2z = 2arrow_forward
- Form 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_forwardFind the value of x if the matrix 1 5 4 is Singular 2 x. 6.arrow_forwardProblems 74–77 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. 74. To graph g(x) = |x + 2| – 3, shift the graph of f(x) = \x| units 76. Solve: logs (x + 3) = 2 units and then 77. Solve the given system using matrices. number Teft/right| number up/down Зх + у + 2z %3 1 75. Find the rectangular coordinates of the point whose polar 2x – 2y + 5z = 5 x + 3y + 2z = -9 coordinates are ( 6, 3arrow_forward
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