Math  /  Algebra

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Part 1 Find the determinant of the following matrix: [623010]\left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]

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: [623010]\left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]
- a=6a = 6 - b=2b = -2 - c=30c = -30 - d=10d = 10

STEP 4

Apply the determinant formula for a 2x2 matrix:
The determinant det(A)\det(A) is given by: det(A)=adbc\det(A) = ad - bc
Substitute the identified elements into the formula: det(A)=(6)(10)(2)(30)\det(A) = (6)(10) - (-2)(-30)

STEP 5

Calculate the determinant:
det(A)=6060\det(A) = 60 - 60 det(A)=0\det(A) = 0
The determinant of the matrix is:
0 \boxed{0}

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