Chapter 5: Q71. (page 228)

Evaluate each determinant $| \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} |$ .

Short Answer

Expert verified

The determinant of $| \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} | = 鈭� 11$ .

Step by step solution

Step 1. Write down the given information.

The given determinant to be evaluated is $| \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} |$ .

Step 2. Concept used.

The determinant of $| \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} | = (a) | \begin{matrix} e & f \\ h & i \end{matrix} | 鈭� (b) | \begin{matrix} d & f \\ g & i \end{matrix} | + (c) | \begin{matrix} d & e \\ g & h \end{matrix} |$ .

Step 3. Calculation.

The determinant of $| \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} |$ is evaluated as: $\begin{matrix} | \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} | = (1) | \begin{matrix} 鈭� 1 & 4 \\ 0 & 2 \end{matrix} | 鈭� (0) | \begin{matrix} 2 & 4 \\ 鈭� 3 & 2 \end{matrix} | + (鈭� 3) | \begin{matrix} 2 & 鈭� 1 \\ 3 & 0 \end{matrix} | \\ = (鈭� 2 鈭� 0) 鈭� (0) 鈭� 3 (0 + 3) \\ = (鈭� 2) 鈭� (0) 鈭� (9) \\ = 鈭� 11 \end{matrix}$

Step 4. Conclusion.

The determinant of $| \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} | = 鈭� 11$ .

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Evaluate each determinant $| \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} |$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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Evaluate each determinant|10鈭�32鈭�14鈭�302|.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Geometry

Logic and Functions

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Evaluate each determinant $| \begin{matrix} 1 & 0 & 鈭� 3 \\ 2 & 鈭� 1 & 4 \\ 鈭� 3 & 0 & 2 \end{matrix} |$ .