TopicName Test - Jacaranda



WorkSHEET 5.1 Matrices and their applications

Name: ___________________________

| |Use matrices to solve the following systems of equations: | 3 |

| |x – y = 1 |[pic] |

| |x + y = 4 |Therefore x = 2[pic] |

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| |x + 2y + 3z = –7 |Using a graphics calculator: |

| |x + y – 2z = 4 |[pic] |

| |x + z = –1 | |

| |Use your graphics calculator for this question. | |

| | |[pic] |

| |y = x – 4 |[pic] |

| |2x + y = 6 | |

| |Verify that C is the inverse of A, where A = [pic] and C = [pic] | |2 |

| |and use this fact to solve |[pic] | |

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| |2x + 3y + z = 10 | | |

| |4x + 6y + 5z = 14 | | |

| |9x + 7y + 8z = 5 |Find the inverse of [pic] | |

| | |and multiply it by [pic] to result in [pic] | |

| | |Therefore x = 4, y = 3 and z = –1. | |

| |Use matrix operations on your graphics calculator to find the inverse | | |

| |of the | | |

| |co-efficient matrix below then use this to solve for x, y and z. | | |

| |x – y = 1 | | |

| |y + z = 2 | | |

| |x – z = 5 | | |

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| |Use Gaussian elimination to solve the following: |Arrange this information into an augmented 4 matrix and perform |

| | |operations to bring it to reduced row echelon form. |

| |x – 2y + z = 6 | |

| |3x + y + z = 5 |[pic] |

| |–x – y – z = –3 | |

| | |[pic] |

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| |2x + y + 2z = 6 | |

| |–x + 2y – z = 7 |[pic] |

| |x – 3y – z = –13 | |

| | |[pic] |

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| |Use the method of Gaussian elimination to find the inverse of the | 4 |

| |following: |[pic] |

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| |[pic] | |

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| |[pic] |[pic] |

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| |Evaluate the following determinants: |[pic] 4 |

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| |[pic] | |

| | |[pic] |

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| |[pic] | |

| | |[pic] |

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| |[pic] | |

| | |[pic] |

| |Show that [pic] = –12 | |

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| |Evaluate the determinant by choosing the simplest row or column by |Expand by row 1: |2 |

| |which to expand: |[pic] | |

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| |[pic] |Expand by row 3: | |

| | |[pic] | |

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| |[pic] | | |

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