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If a 4x4 matrix `A` with rows` v_1,v_2,v_3` and `v_4` has determinant `det(A) = -8`...
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High School Teacher
We will use the following two properties (axioms) of determinant:
1) Multiplying a row by `k` multiplies the determinant by `k.`
`det(v_1,ldots,k cdot v_i,ldots,v_n)=k cdot det(v_1,ldots,v_i,ldots,v_n)`
2) Adding one row multiplied by `k` to another row does not change the determinant.
`det(v_1,ldots,v_i+k cdot v_j,ldots,v_n)=det(v_1,ldots,v_i,ldots,v_n)`
Let's first apply second property.
Now we use the first property.
`6(-8)=-48` <--- Your solution
Posted by tiburtius on April 26, 2013 at 4:48 PM (Answer #1)
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