Chapter 4: Q. 415 (page 485)

Evaluate the determinant by
expanding by minors:
$|\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}|$

Short Answer

Expert verified

The value of determinant is 7.

Step by step solution

Step 1. given Information.

Given square matrix:

$|\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}|$

Step 2. Write the concept.

To find determinant of $3 \times 3$ matrix using the minors we use the formula,

$|\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix}| = a_{1} |\begin{matrix} b_{2} & c_{2} \\ b_{3} & c_{3} \end{matrix}| - b_{1} |\begin{matrix} a_{2} & c_{2} \\ a_{3} & c_{3} \end{matrix}| + c_{1} |\begin{matrix} a_{2} & b_{2} \\ a_{3} & b_{3} \end{matrix}|$

expanding the minors can be done by selecting any row or column. Since 0 is present in second row and third column expanding by it will make calculation easier.

Step 3. Calculation.

Expand using third row. $|\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}| = - 1 |\begin{matrix} - 2 & - 2 \\ - 1 & 4 \end{matrix}| + 0 |\begin{matrix} 3 & - 2 \\ 2 & 4 \end{matrix}| - 3 |\begin{matrix} 3 & - 2 \\ 2 & - 1 \end{matrix}| = - 1 [(- 2) (4) - (- 2) (- 1) - 3 [(3) (- 1) - (- 2) (2)] = - 1 [- 8 - 2] - 3 [- 3 + 4] = - 1 [- 10] - 3 [1] = 10 - 3 = 7$

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Evaluate the determinant by
expanding by minors:
$|\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}|$

Short Answer

Step by step solution

Step 1. given Information.

Step 2. Write the concept.

Step 3. Calculation.

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Evaluate the determinant byexpanding by minors:3-2-22-14-10-3

Short Answer

Step by step solution

Step 1. given Information.

Step 2. Write the concept.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Calculus

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Evaluate the determinant by
expanding by minors:
$|\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}|$