Question

Evaluate the following determinant using
3 4 2
2 1 3
-1 2 4
Using Laplace expansion method​

Answer 1

Given :

• Evaluate the following determinant using Laplace expansion method :

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

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To Find :

• The determinant |A| values =?

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Solution:

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

By using Laplace expansion method

Expanding determinant R1 along we get,

$\\ \implies\sf{|A| =3(1 \times 4-3 \times 2)-4(2 \times 4- 3 \times -1)+2(2 \times 2- 1 \times -1)}$

$\\ \implies\sf{|A| =3(4-6)-4(8+3)+2(4+1)}$

$\\ \implies\sf{|A| =3(-2)-4(11)+2(5)}$

$\\ \implies\sf{|A|=-6-44+10}$

$\\ \implies\sf{|A|=-50+10}$

$\\ \implies\sf{|A|=-40}$

$\\ \implies\boxed{\sf{|A|=-40}}$

The value of determinant |A| is -40