Chapter 5: Q71. (page 228)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Write down the given information.

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

Step 2. Concept used.

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

Step 3. Calculation.

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

Step 4. Conclusion.

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

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

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|10−32−14−302|.

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

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