a) Show that is it linear in the first column.
b) Show that it is alternating when you switch the first and second column.
(// denotes the next row in the matrix)
I'm not sure how to prove this, any help is great. Thanks.
a) It says that if you multiply the first column by a number k, then the determinant also get multplied by k. To prove this, multiply x1,x2,x3 by k and see what happens to determinant.
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a) It says that if you multiply the first column by a number k, then the determinant also get multplied by k. To prove this, multiply x1,x2,x3 by k and see what happens to determinant.
It also says that if you replace x1, x2, x3 by a1+ b1, a2+ b2, a3+ b3, you will get the determinant with a1, a2, a3 plus the determinant with b1, b2, b3.
Tedious calculation but just basic algebra.
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3 x 3 Matrix 
Linear Mode
