Simplify the Matrix [[x,0,-1],[3,-9,x],[x,0,6]]=9

Problem

|[x,0,−1],[3,−9,x],[x,0,6]|=9

Solution

1. Identify the operation as finding the determinant of a 3×3 matrix and solving for x

2. Expand the determinant along the second column, which contains two zeros, to simplify the calculation.

3. Calculate the cofactor of the element −9 which is located at row 2, column 2.

(−9)⋅|[x,−1],[x,6]|=9

4. Evaluate the 2×2 determinant using the formula a*d−b*c

−9*(6*x−(−x))=9

5. Simplify the expression inside the parentheses.

−9*(7*x)=9

6. Solve the resulting linear equation for x

−63*x=9

7. Divide both sides by −63 to isolate x

x=−9/63

8. Reduce the fraction to its simplest form.

x=−1/7

Final Answer

|[x,0,−1],[3,−9,x],[x,0,6]|=9⇒x=−1/7

Want more problems? Check here!