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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]
[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]
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