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



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Determine whether the mapping \( T \) is a linear transformation, and if so, find its kernel.
\( T: M_{22} \rightarrow R \),
Determine whether the mapping \( T \) is a linear transformation, and if so, find its ker
\( T: M_{22} \rightarrow R \), wher
(b) \( T\left(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\right)=a^{2}+\mathrm{d}^{2} \)
Pick the appropriate ans
eTextbook and Media
(b) \( T\left(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\right)=a^{2}+d^{2} \)
Pick the appr
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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(a) Given that, the mapping T:M22?R is defined by T([abcd])=8a?6b+c?d. Let A=[a1b1c1d1],B=[a2b2c2d2]?M22. Then T(A)=8a1
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