In Problems 1–6 write the given linear system in matrix form.
3.
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- Problem 8. Determine whether the 2×2 matrix (1) is in the span of {(18), (11),(18)}. 1arrow_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_forwardSolving 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_forward
- Homogeneous 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.arrow_forward4x — у 3 3. Express the following system of equations as a matrix equation of the form • x - y = 4 2x – y = 0 x + y+ 2z = -2 4x + 2y – z = -8 y + = 1 3arrow_forward
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- Problem 5. Let A be an n x n real symmetric matrix that satisfies A³ = -A. Show that A must be the zero matrix.arrow_forward4. Solve the linear system of equations below via matrices showing your work in detail. X1 + X2 Хз + 3 Х4 = 1 X2 Хз 4 Х4 X1 + 2 х2 - 2 Хз — Ха %3D 4x1 + 7 x2 – 7x3 = 9arrow_forwardHomework 12: Question 4arrow_forward
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