Q. 4 How is the determinant of a 3 脳... [FREE SOLUTION]

Chapter 10: Q. 4 (page 823)

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

Step by step solution

Step 1. Given Information

We have to find how the determinant of a 3 脳 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

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

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How is the determinant of a 3 脳 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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91影视

How is the determinant of a 3 脳 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

Probability and Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

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