MATH Integrated Math III  - Unit 12: Solving Systems With Matrix Equations
For the first four problems calculate the determinant, and then determine if the matrix has an inverse.

1) Calculate the determinant to determine if the matrix has an inverse. (a) State the determinant. (b) If the matrix has an inverse, write true; if not, write false.

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2) Calculate the determinant to determine if the matrix has an inverse. (a) State the determinant. (b) If the matrix has an inverse, write true; if not, write false.

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3) Calculate the determinant to determine if the matrix has an inverse. (a) State the determinant. (b) If the matrix has an inverse, write true; if not, write false.

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4) Calculate the determinant to determine if the matrix has an inverse. (a) State the determinant. (b) If the matrix has an inverse, write true; if not, write false.

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For the next two problems determine if the two matrices are inverses of each other, and then select true or false.

5) True or False? These matrices are inverses of each other.

6) True or False? These matrices are inverses of each other.

For the next two problems find the inverse matrix, if it exists. If the inverse does not exist, write “no inverse”. If the inverse does exist, just type the answer (by rows) without the matrix symbols.

7) Find the inverse matrix, if it exists.

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8) Find the inverse matrix, if it exists.

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For the next two problems write the matrix equation that represents each system. Type the answer, by rows, without the matrix symbols.

9) Write the matrix equation that represents this system. Just type the answer, by rows, without the matrix symbols.

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10) Write the matrix equation that represents this system. Just type the answer, by rows, without the matrix symbols.

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For the next two problems write the system of equations represented by each matrix equation.

11) Write the system of equations represented by this matrix equation.

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12) Write the system of equations represented by this matrix equation.

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For the next two problems solve each system of equations by using matrices.

13) Use matrices to solve the following system of equations:

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14) Use matrices to solve the system of equations.

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Short Answer

15) Which of the following matrices have a determinant? Explain.

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