# (Solved): please solve allit's one question Determine whether the mapping $$T$$ is a linear transformation, ...

it's one question

Determine whether the mapping $$T$$ is a linear transformation, and if so, find its kernel. $$T: M_{22} \rightarrow R$$, where (a) $$T\left(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\right)=8 a-6 b+c-d$$ Pick the appropriate answer from below. Kernel of $$T$$ is of the form: $\begin{array}{l} {\left[\begin{array}{cc} 8 a-6 b+c & b \\ c & a \end{array}\right]} \\ {\left[\begin{array}{cc} a & b \\ c & 8 a-6 b+c \end{array}\right]} \\ \end{array}$ Not applicable $\left[\begin{array}{cc} a & c \\ b & 8 a-6 b+c \end{array}\right]$ (b) $$T\left(\left[\begin{array}{ll}a & b\end{array}\right]\right)=a^{2}+d^{2}$$ Determine whether the mapping $$T$$ is a linear transformation, and if so, find its ker $$T: M_{22} \rightarrow R$$, where (a) $$T\left(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\right)=8 a-6 b+c-d$$ Pick the appropriate answer from below. $\begin{array}{l} {\left[\begin{array}{cc} 8 a-6 b+c & b \\ c & a \end{array}\right]} \\ {\left[\begin{array}{cc} a & b \\ c & 8 a-6 b+c \end{array}\right]} \end{array}$ Not applicable $\left[\begin{array}{cc} a & c \\ b & 8 a-6 b+c \end{array}\right]$ (b) $$T\left(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\right)=a^{2}+d^{2}$$ (b) $$T\left(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\right)=a^{2}+\mathrm{d}^{2}$$ Pick the appropriate answer from below. Kernel of $$T$$ is of the form: $\begin{array}{l} {\left[\begin{array}{ll} a & d \\ c & b \end{array}\right]} \\ {\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]} \end{array}$ Not applicable $\left[\begin{array}{ll} d & c \\ b & a \end{array}\right]$ eTextbook and Media (b) $$T\left(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\right)=a^{2}+d^{2}$$ Pick the appropriate answer from below. $\begin{array}{l} {\left[\begin{array}{ll} a & d \\ c & b \end{array}\right]} \\ {\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]} \end{array}$ Not applicable $\left[\begin{array}{ll} d & c \\ b & a \end{array}\right]$

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