Translate each of the following augmented matrices into a system of equations. Write the solution set in parametric vector form. [103 2 [10 0 (a) 0 1 0 -5 (b) 0 1 0 00 0 0 2 7 00 1 -8 [10 5 0 (c) 0 1 -20 00 0 1 1 (d) 0 200 0 -1 4 1 3 5 0 0 0 00 00 [] 0 1 (e)

For this exercise assume that the matrices are all nxn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer. If the equation Ax = b has at least one solution for each b in R, then the solution is unique for each b. Choose the correct answer below. A. The statement is true. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R", then matrix A is invertible. If A is invertible, then according to the invertible matrix theorem the solution is unique for each b. OB. The statement is true, but only for x 0. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R, then the equation Ax = 0 does not only have the trivial solution. OC. The statement is false. By the…

Use Cramer's Rule to solve the 3 x 3 matrix A- 3B + 7Z = 13 A +B+Z = 1 A – 2B + 3Z = 4

Fill in the blanks of the resulting matrix after the given row operation is performed: -1 8 3 -1 7 -4R₁ 3 R₁ 381 3 -1 8 R₂+3R₁ -1 7 -4 -1 8 R₁-4R₂ 7 R₂ R₁

Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. [:::) 1 2 0 - 3 3 6 0 - 9 x=x+x+xO X= X2 + X3 +X4 (Type an integer or fraction for each matrix element.)

Linear Algebra. Please write your answer clearly. Thanks.