Examine whether a transformation is linear. Find the image and kernel of a linear transformation. Examine whether a linear transformation is an isomorphism. Find out which of the transformation are linear. For those that are linear, determine whether they are isomorphisms. $$T(c)=c\left[\begin{array}{ll} 2 & 3 \\ 4 & 5 \end{array}\right] \text { from } \mathbb{R} \text { to } \mathbb{R}^{2 \times 2}$$
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Step 1: To determine if the transformation is linear, we need to check if it satisfies the two properties of linearity. Show more…
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