I am an Engineer from a top-notch institute. I have vast experience of teaching applied science subjects including Physics, Math's, Chemistry to students across the globe.
define the linear transformation $T$ by $T(x)=A x .$ Find (a) the kernel of $T$ and (b) the range of $T$.$$ A=\left[\begin{array}{rr} 1 & 3 \\ -1 & -3 \\ 2 & 2 \end{array}\right] $$
define the linear transformation $T$ by $T(x)=A x .$ Find (a) the kernel of $T$ and (b) the range of $T$.$$ A=\left[\begin{array}{rr} 1 & 1 \\ -1 & 2 \\ 0 & 1 \end{array}\right] $$
define the linear transformation $T$ by $T(\mathbf{x})=A \mathbf{x} . \text { Find }(\mathbf{a}) \text { ker( } T),(\mathbf{b})$ nullity $(T),(\mathbf{c})$ range $(T)$ and (d) rank(T).$$ A=\left[\begin{array}{rr} -1 & 1 \\ 1 & 1 \end{array}\right] $$
define the linear transformation $T$ by $T(\mathbf{x})=A \mathbf{x} . \text { Find }(\mathbf{a}) \text { ker( } T),(\mathbf{b})$ nullity $(T),(\mathbf{c})$ range $(T)$ and (d) rank(T).$$ A=\left[\begin{array}{rr} 3 & 2 \\ -9 & -6 \end{array}\right] $$
define the linear transformation $T$ by $T(\mathbf{x})=A \mathbf{x} . \text { Find }(\mathbf{a}) \text { ker( } T),(\mathbf{b})$ nullity $(T),(\mathbf{c})$ range $(T)$ and (d) rank(T).$$ A=\left[\begin{array}{rr} 5 & -3 \\ 1 & 1 \\ 1 & -1 \end{array}\right] $$
