0000:00:00:00:00Start20Number 20ExplanationGiven matrix A=(2−2x−11)A = \begin{pmatrix} 2 & -2 \\ x-1 & 1 \end{pmatrix}A=(2x−1−21). If det(A)=4\det(A) = 4det(A)=4, then the value of xxx is222111000−1-1−1−2-2−2ExplanationWe are given matrix AAA as follows: A=(2−2x−11)A = \begin{pmatrix} 2 & -2 \\ x-1 & 1 \end{pmatrix}A=(2x−1−21) It is known that the determinant of matrix AAA is 444. The determinant formula for a 2×22 \times 22×2 matrix like (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}(acbd) is ad−bcad - bcad−bc. Calculating the Determinant We will calculate the determinant of matrix AAA and set it equal to 444: det(A)=(2)(1)−(−2)(x−1)4=2−(−2x+2)4=2+2x−24=2xx=42x=2\begin{aligned} \det(A) &= (2)(1) - (-2)(x-1) \\ 4 &= 2 - (-2x + 2) \\ 4 &= 2 + 2x - 2 \\ 4 &= 2x \\ x &= \frac{4}{2} \\ x &= 2 \end{aligned}det(A)444xx=(2)(1)−(−2)(x−1)=2−(−2x+2)=2+2x−2=2x=24=2 So, the value of xxx is 222.
20Number 20ExplanationGiven matrix A=(2−2x−11)A = \begin{pmatrix} 2 & -2 \\ x-1 & 1 \end{pmatrix}A=(2x−1−21). If det(A)=4\det(A) = 4det(A)=4, then the value of xxx is222111000−1-1−1−2-2−2ExplanationWe are given matrix AAA as follows: A=(2−2x−11)A = \begin{pmatrix} 2 & -2 \\ x-1 & 1 \end{pmatrix}A=(2x−1−21) It is known that the determinant of matrix AAA is 444. The determinant formula for a 2×22 \times 22×2 matrix like (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}(acbd) is ad−bcad - bcad−bc. Calculating the Determinant We will calculate the determinant of matrix AAA and set it equal to 444: det(A)=(2)(1)−(−2)(x−1)4=2−(−2x+2)4=2+2x−24=2xx=42x=2\begin{aligned} \det(A) &= (2)(1) - (-2)(x-1) \\ 4 &= 2 - (-2x + 2) \\ 4 &= 2 + 2x - 2 \\ 4 &= 2x \\ x &= \frac{4}{2} \\ x &= 2 \end{aligned}det(A)444xx=(2)(1)−(−2)(x−1)=2−(−2x+2)=2+2x−2=2x=24=2 So, the value of xxx is 222.
