Math  /  Algebra

Question11. Galoulate the determinant. [5231]\left[\begin{array}{ll} 5 & 2 \\ 3 & 1 \end{array}\right] 1 11 0 11-11 1-1

Studdy Solution

STEP 1

1. The matrix given is a 2x2 matrix.
2. The determinant of a 2x2 matrix [abcd]\left[\begin{array}{cc} a & b \\ c & d \end{array}\right] is calculated using the formula: adbcad - bc.

STEP 2

1. Identify the elements of the matrix.
2. Apply the determinant formula for a 2x2 matrix.
3. Calculate the determinant.

STEP 3

Identify the elements of the matrix:
Given matrix: [5231]\left[\begin{array}{cc} 5 & 2 \\ 3 & 1 \end{array}\right]
Here, a=5a = 5, b=2b = 2, c=3c = 3, and d=1d = 1.

STEP 4

Apply the determinant formula for a 2x2 matrix:
The determinant is calculated as: det=adbc \text{det} = ad - bc

STEP 5

Substitute the identified elements into the formula and calculate:
det=(5)(1)(2)(3) \text{det} = (5)(1) - (2)(3) det=56 \text{det} = 5 - 6 det=1 \text{det} = -1
The determinant of the matrix is:
1 \boxed{-1}

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