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Find the determinant of the matrix

[tex]\[ \left[\begin{array}{cc}-2 & 5 \\ 1 & 4\end{array}\right] \][/tex]


Sagot :

To find the determinant of a 2x2 matrix, we can use a straightforward formula. For any 2x2 matrix of the form:

[tex]\[ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \][/tex]

The determinant is calculated as:

[tex]\[ \text{det} = (a \cdot d) - (b \cdot c) \][/tex]

Given the matrix:

[tex]\[ \begin{bmatrix} -2 & 5 \\ 1 & 4 \end{bmatrix} \][/tex]

We can identify the elements as follows:
- [tex]\( a = -2 \)[/tex]
- [tex]\( b = 5 \)[/tex]
- [tex]\( c = 1 \)[/tex]
- [tex]\( d = 4 \)[/tex]

Now we substitute these values into the determinant formula:

[tex]\[ \text{det} = (-2 \cdot 4) - (5 \cdot 1) \][/tex]

First, calculate the products:

[tex]\[ -2 \cdot 4 = -8 \][/tex]

[tex]\[ 5 \cdot 1 = 5 \][/tex]

Then, subtract the second product from the first:

[tex]\[ -8 - 5 = -13 \][/tex]

Therefore, the determinant of the matrix is:

[tex]\[ \boxed{-13} \][/tex]