Question
define the linear transformation $T$ by $T(x)=A x .$ Find (a) the kernel of $T$ and (b) the range of $T$.$$ A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right] $$
Step 1
In this case, we are looking for all vectors $x = (x_1, x_2)$ such that $Ax = 0$, where $A$ is the given matrix. This gives us the system of equations: \begin{align*} x_1 + 2x_2 &= 0, \\ 3x_1 + 4x_2 &= 0. \end{align*} Show more…
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