Victoria D.

asked • 04/06/20

If A and B are any matrices of order 2×1, show that the product ABt has no inverse

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Arturo O. answered • 04/06/20

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A = |x|

|y|


B = |z|

|w|


Bt = |z w|


If is sufficient to show that


det(ABt) = 0


ABt = |xz xw|

|yz yw|


det(ABt) = xzyw - yzxw = 0

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Arturo O.

An interesting problem, I might add.
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04/06/20

Victoria D.

Thanks Arturo, just confirming the reason ABt has no inverse is because the determinant is 0. The conclusion drawn to by a*d-b*c?
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04/06/20

Arturo O.

You are welcome, Victoria. For an inverse to exist, the determinant cannot be zero. You can see that in this problem it will be zero regardless of the choices of matrix elements.
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04/06/20

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