Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation.
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Question

Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation.
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Quizplus · Accepted Answer

We are given the matrix equation:
| 2 4 6 |   | x |   | 22 |
| 1 3 5 | x | y | = | 14 |
| 7 8 9 |   | z |   | 41 |

Substituting x=11, y=13, z=20, we get:
| 2 4 6 |   | 11 |   | 22 |
| 1 3 5 | x | 13 | = | 14 |
| 7 8 9 |   | 20 |   | 41 |

Using matrix multiplication, we can verify that this equation is satisfied:
| 2*11 + 4*13 + 6*20 |   | 22 |   | 22 |
| 1*11 + 3*13 + 5*20 | x | 13 | = | 14 |
| 7*11 + 8*13 + 9*20 |   | 20 |   | 41 |

Simplifying the left-hand side, we get:
| 262 |   | 22 |   | 22 |
| 292 | x | 13 | = | 14 |
| 523 |   | 20 |   | 41 |

So, the given values of x=11, y=13, z=20 satisfy the matrix equation. Therefore, the answer is A.

Substitute the Given Values of X, Y, and Z into the Matrix