Question

Find the determinant of the matrix:
(5-2 3)
(4-1-5)
(6 7 9)

Answer 1

Answer:

224

Step-by-step explanation:

5(-1*9-(-5*7))+2(36+30)+3(28+6)

5(26)+2(96)+3(34)

130+192+102

224

Answer 2

Answer:

The determinant of the matrix is 364.

Step-by-step explanation:

The determinant of a matrix exists in the scalar value calculated for a conveyed square matrix. Linear algebra values with the determinant exist calculated utilizing the components of a square matrix. It can be regarded as the scaling aspect for the transformation of a matrix.

Given:

$\left[\begin{array}{ccc}5 & -2 & 3 \\ 4 & -1 & -5 \\ 6 & 7 & 9\end{array}\right]$

To find:

the determinant of the matrix.

Step 1

Let

$A= \left[\begin{array}{ccc}5 & -2 & 3 \\ 4 & -1 & -5 \\ 6 & 7 & 9\end{array}\right]$

be a matrix.

then | A | is

$\left|\begin{array}{ccc}5 & -2 & 3 \\ 4 & -1 & -5 \\ 6 & 7 & 9\end{array}\right|=5\left|\begin{array}{cc}-1 & -5 \\ 7 & 9\end{array}\right|+2\left|\begin{array}{cc}4 & -5 \\ 6 & 9\end{array}\right|+3\left|\begin{array}{cc}4 & -1 \\ 6 & 7\end{array}\right|$

Step 2

Simplifying the above equation, we get

= 5(-9 + 35) + 2(36 + 30) + 3(28 + 6)

= 5(26) + 2(66) + 3(34)

equating,

= 130 + 132 + 102

= 364

Therefore, the determinant of the matrix is 364.

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