Question

Evaluate the following determinant

24 3 3
56 7 17
73 9 22​

Answer 1

The determinant of the given matrix is equals to 30.

Step-by-step explanation:

The detailed explanation has been given in the attached images.

Answer 2

Determinant of

$\left| \begin{array}{ccc}\bf 24&\bf 3&\bf 3\\\bf 56&\bf 7&\bf 17\\\bf 73&\bf 9&\bf 22\end{array}\right| \:\text{is}\: \bf 30$

Given:

• $\left|\begin{array}{ccc}24&3&3\\56&7&17\\73&9&22\end{array}\right|$

To find:

• Evaluate the determinant.

Solution:

Formula/Concept to be used:

• Determinant of a 3×3 matrix is shown below:
• $\left|\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right|= a(ei - fh) - b(di - gf) + c(dh - eg)$
• To simplify the calculations, one can apply elementary row and column operations.

Step 1:

Apply some elementary column operations.

$C_1=>C_1-8C_3\\ C_2=>C_2-C_3$

$\left|\begin{array}{ccc}24 - 24&3 - 3&3\\56 -136&7 - 17&17\\73 -176&9 - 22&22\end{array}\right|$

or

$\left|\begin{array}{ccc}0&0&3\\-80 &- 10&17\\-103& - 13&22\end{array}\right|$

Apply

$C_1=>C_1 - 8C_2$

$\left|\begin{array}{ccc}0&0&3\\0 &-10&17\\1& -13& 22\end{array}\right|$

Step 2:

Expand the determinant along first row.

$\left|\begin{array}{ccc}0&0&3\\5 &0&17\\7& 1& 22\end{array}\right| = 0 - 0 + 3(0+10)$

$= 30$

Thus,

Determinant of

$\left| \begin{array}{ccc}\bf 24&\bf 3&\bf 3\\\bf 56&\bf 7&\bf 17\\\bf 73&\bf 9&\bf 22\end{array}\right|\: \text{is}\:\bf 30$

Learn more:

1) solve the determinant by using ementary operations

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2) a b c

-a b c

-a -b c

Evaluate

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