In Exercises 1–14, perform each matrix row operation and write the new matrix.
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- In Exercises 5–8, determine if the columns of the matrix form a linearly independent set. Justify each answer.arrow_forwardSolve each system in Exercises 1–4 by using elementary rowoperations on the equations or on the augmented matrix. Followthe systematic elimination procedure described in this section.arrow_forwardUnless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answersarrow_forward
- In Exercises 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_forwardIn Exercises 5–8, use the definition of Ax to write the matrix equation as a vector equation, or vice versa. 5. 5 1 8 4 -2 -7 3 −5 5 -1 3 -2 = -8 - [18] 16arrow_forwardUse Cramer’s rule to compute the solutions of the systems in Exercises 1–6.arrow_forward
- In Exercises 19–20, solve the matrix equation for X. 1 -1 1 -1 5 7 8. 19. 2 3 0| X = 4 -3 1 1 3 5 -7 2 1 -arrow_forward[M] In Exercises 37–40, determine if the columns of the matrix span R4.arrow_forwardIn Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.arrow_forward
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