6Number 6ExplanationGiven the matrix A=(2x−2−11)A = \begin{pmatrix} 2 & x-2 \\ -1 & 1 \end{pmatrix}A=(2−1x−21). If det(A)=8\det(A) = 8det(A)=8, then the value of xxx is ...444222000−2-2−2888ExplanationGiven the matrix A=(2x−2−11)A = \begin{pmatrix} 2 & x-2 \\ -1 & 1 \end{pmatrix}A=(2−1x−21). We need to find the value of xxx if det(A)=8\det(A) = 8det(A)=8. The determinant of a 2×22 \times 22×2 matrix is calculated using the formula ad−bcad - bcad−bc. det(A)=(2)(1)−(x−2)(−1)\det(A) = (2)(1) - (x-2)(-1)det(A)=(2)(1)−(x−2)(−1) We know that det(A)=8\det(A) = 8det(A)=8, so: 8=2−(−(x−2))8=2+(x−2)8=2+x−28=x\begin{align*} 8 &= 2 - (-(x-2)) \\ 8 &= 2 + (x-2) \\ 8 &= 2 + x - 2 \\ 8 &= x \end{align*}8888=2−(−(x−2))=2+(x−2)=2+x−2=x Thus, the value of xxx is 888.
