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| − | <span class="exam">Consider the matrix <math style="vertical-align: -31px">A= | + | <span class="exam">If <math style="vertical-align: 0px">A</math> is an <math style="vertical-align: 0px">n\times n</math> matrix such that <math style="vertical-align: -4px">AA^T=I,</math> what are the possible values of <math style="vertical-align: 0px">\text{det }A?</math> |
| − | \begin{bmatrix}
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| − | 1 & -4 & 9 & -7 \\
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| − | -1 & 2 & -4 & 1 \\
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| − | 5 & -6 & 10 & 7
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| − | \end{bmatrix}</math> and assume that it is row equivalent to the matrix
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| − | ::<math>B=
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| − | \begin{bmatrix}
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| − | 1 & 0 & -1 & 5 \\
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| − | 0 & -2 & 5 & -6 \\
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| − | 0 & 0 & 0 & 0
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| − | \end{bmatrix}.</math>
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| − | <span class="exam">(a) List rank <math style="vertical-align: 0px">A</math> and <math style="vertical-align: 0px">\text{dim Nul }A.</math>
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| − | <span class="exam">(b) Find bases for <math style="vertical-align: 0px">\text{Col }A</math> and <math style="vertical-align: 0px">\text{Nul }A.</math> Find an example of a nonzero vector that belongs to <math style="vertical-align: -5px">\text{Col }A,</math> as well as an example of a nonzero vector that belongs to <math style="vertical-align: 0px">\text{Nul }A.</math>
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Revision as of 19:17, 9 October 2017
If 
is an 
matrix such that 
what are the possible values of 
Solution:
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