Chapter 10: Q. 4 (page 823)

How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectors $u = (u_{1}, u_{2}, u_{3}) and v = (v_{1}, v_{2}, v_{3})$ ?

Short Answer

Expert verified

The determinant of a 3 × 3 matrix is $u \times v = \det [\begin{matrix} i & j & k \\ u_{1} & u_{2} & u_{3} \\ v_{1} & v_{2} & v_{3} \end{matrix}]$ .

Step by step solution

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 vectors $u = (u_{1}, u_{2}, u_{3}) and v = (v_{1}, v_{2}, v_{3})$ .

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

$u = (u_{1}, u_{2}, u_{3}) v = (v_{1}, v_{2}, v_{3}) u = u_{1} i + u_{2} j + u_{3} k v = v_{1} i + v_{2} j + v_{3} k$

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

$u \times v = \det [\begin{matrix} i & j & k \\ u_{1} & u_{2} & u_{3} \\ v_{1} & v_{2} & v_{3} \end{matrix}]$

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How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectors $u = (u_{1}, u_{2}, u_{3}) and v = (v_{1}, v_{2}, v_{3})$ ?

Short Answer

Step by step solution

Step 1. Given Information

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

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

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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

Step by step solution

Step 1. Given Information

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectors $u = (u_{1}, u_{2}, u_{3}) and v = (v_{1}, v_{2}, v_{3})$ ?