Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Algebra Algebra of Linear Transformations
Let \(C=\left[\left(\begin{array}{l} 1 \\ 2 \end{array}\right),\left(\begin{array}{l} 2 \\ 1 \end{array}\right)\right]\) be a basis of ℝ2 and T: ℝ2 →ℝ2 be defined by \(T\left(\begin{array}{l} x \\ y \end{array}\right)=\left(\begin{array}{l} x+y \\ x-2 y \end{array}\right)\) If T[C] represents the matrix of T with respect to the basis C, then which among the following is true?
1
\(T[C]=\left[\begin{array}{rr} -3 & -2 \\ 3 & 1 \end{array}\right]\)
2
\(T[C]=\left[\begin{array}{rr} 3 & -2 \\ -3 & 1 \end{array}\right]\)
3
\(T[C]=\left[\begin{array}{rr} -3 & -1 \\ 3 & 2 \end{array}\right]\)
4
\(T[C]=\left[\begin{array}{rr} -3 & 1 \\ 3 & 2 \end{array}\right]\)
5
Question Not Attempted