Find the Determinant [[-4,30+2k],[-12,-10+2k]]

Problem

det(−4)

Solution

1. Identify the formula for the determinant of a 2×2 matrix [[a,b],[c,d]] which is a*d−b*c

2. Substitute the values from the matrix into the formula: a=−4 b=30+2*k c=−12 and d=−10+2*k

3. Set up the expression for the determinant.

det(=)*(−4)*(−10+2*k)−(−12)*(30+2*k)

4. Distribute the constants into the binomials.

(−4)*(−10+2*k)=40−8*k

−(−12)*(30+2*k)=12*(30+2*k)=360+24*k

5. Combine the resulting terms.

40−8*k+360+24*k

6. Simplify by adding like terms.

400+16*k

Final Answer

det(−4)=16*k+400

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