Chapter 3: Q9P (page 95)

Show without computations that the following determinant is equal to zero. Hint: Consider the effect of interchanging rows and columns.
$| \begin{matrix} 0 & 2 & - 3 \\ - 2 & 0 & 4 \\ 3 & - 4 & 0 \end{matrix} |$

Short Answer

Expert verified

It has been proved that the determinant is zero.

Step by step solution

Results used

Facts used about determinants:

If each element of one row of a determinant is multiplied by a number k, the determinant becomes k times.
The value of a determinant remains the same if rows are written as columns and columns as rows.

Show that the determinant is zero

Consider, $D = |\begin{matrix} 0 & 2 & - 3 \\ - 2 & 0 & 4 \\ 3 & - 4 & 0 \end{matrix}|$

Write each row as a column and vice versa, using fact 2 as:

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

Multiply each row by -1. So Using fact 1, the determinant is

$D = {(- 1)}^{3} |\begin{matrix} 0 & 2 & - 3 \\ - 2 & 0 & - 4 \\ 3 & - 4 & 0 \end{matrix}| = - D$

Thus,

$D + D = 0 2 D = 0 D = 0$

Hence, determinant is zero.

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Show without computations that the following determinant is equal to zero. Hint: Consider the effect of interchanging rows and columns.
$| \begin{matrix} 0 & 2 & - 3 \\ - 2 & 0 & 4 \\ 3 & - 4 & 0 \end{matrix} |$

Short Answer

Step by step solution

Results used

Show that the determinant is zero

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Show without computations that the following determinant is equal to zero. Hint: Consider the effect of interchanging rows and columns.|02-3-2043-40|

Short Answer

Step by step solution

Results used

Show that the determinant is zero

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Linear Momentum

Physics of Motion

Solid State Physics

Dynamics

Classical Mechanics

Study anywhere. Anytime. Across all devices.

Show without computations that the following determinant is equal to zero. Hint: Consider the effect of interchanging rows and columns.
$| \begin{matrix} 0 & 2 & - 3 \\ - 2 & 0 & 4 \\ 3 & - 4 & 0 \end{matrix} |$