Find the Determinant

Problem

det(√(,2))

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 given matrix into the formula where a=√(,2) b=2√(,3) c=√(,6) and d=5

3. Set up the calculation for the determinant.

det(=)*(√(,2))*(5)−(2√(,3))*(√(,6))

4. Simplify the first term.

(√(,2))*(5)=5√(,2)

5. Simplify the second term by multiplying the radicals.

(2√(,3))*(√(,6))=2√(,18)

6. Factor the radical √(,18) into √(,9⋅2) to simplify further.

2√(,18)=2⋅3√(,2)

2⋅3√(,2)=6√(,2)

7. Subtract the simplified terms to find the final value.

5√(,2)−6√(,2)=−√(,2)

Final Answer

det(√(,2))=−√(,2)

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