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How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectorsu=(u1,u2,u3)andv=(v1,v2,v3)?

Short Answer

Expert verified

The determinant of a 3 × 3 matrix is u×v=detijku1u2u3v1v2v3.

Step by step solution

01

Step 1. Given Information 

We have to find how the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectorsu=(u1,u2,u3)andv=(v1,v2,v3).

02

Step 2. The given two vectors are u=(u1,u2,u3) and v=(v1,v2,v3).

u=(u1,u2,u3)v=(v1,v2,v3)u=u1i+u2j+u3kv=v1i+v2j+v3k

03

Step 3. Now the determinant of a 3 × 3 matrix is

u×v=detijku1u2u3v1v2v3

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