In Problems 1–6 write the given linear system in matrix form.
2.
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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_forwardProblem 4. Let A= = 9 0 0 4 3 3 1 Find a matrix B such that B2 = A.arrow_forward19. Find the reduced row echelon form of the matrix 2 10 0 1 1 1 -1 1 1 None of the given options 1 0 1 2 0 1 -2 -3 3 5arrow_forward
- 1.2. Find a matrix A for which a1,1 = a2,2 = a3,3 = 1, but elimination (with no row exchanges) produces two negative pivots (the first pivot is 1).arrow_forwardSuppose B and D are the following two bases for P2: B=|4x²-4x-2, ³-4x−2, 3x²-x, −3x−3] D= [−3x−3, x²+x+1» x²+1} Find the change matrix PD-B- 000 000 0 0 0 PD-B =arrow_forwardSuppose that 2 3 Solve the linear system Ax = b for each of the following matrices b: 8 (b) 15 (a)arrow_forward
- 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z? – 2xy – 2xz – 2yz, and classify it.arrow_forward5 -3 2 15. Investigate the type of the square matrix A =| 15 -9 6 10 -6 4arrow_forward2. Suppose 3 2 1 A =3 4 2 3 2 2 (1) Find the LU factorization of the matrix A; (2) Using the LU factorization to solve the system of equations Ax =b where b=[4 5 s.arrow_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_forward6. Give an example of two matrices, A and B, neither of which contains any zero entries whose product AB = 0, the zero matrix.arrow_forwardFor what value of "c" is the following matrix non-invertible? C 2 1 -1 5 4 C 3 0 Oc = - 1 3 Oc = -3 Oc = 3 %D Oc = } 3arrow_forward
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