Explain why parallelograms are always quadrilaterals but quadrilaterals are sometimes parallelograms
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I'll go out on a limb and suppose you're given the matrix
and you're asked to find the determinant of
, where
and given that
.
There are two properties of the determinant that come into play here:
(1) Whenever a single row/column is scaled by a constant
, then the determinant of the matrix is scaled by that same constant;
(2) Adding/subtracting rows does not change the value of the determinant.
Taken together, we have that
and you're asked to find the determinant of
and given that
There are two properties of the determinant that come into play here:
(1) Whenever a single row/column is scaled by a constant
(2) Adding/subtracting rows does not change the value of the determinant.
Taken together, we have that