Exercise · ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-009 · ★★★ Advanced
The matrix of \(T\) in the standard bases is \(\begin{pmatrix}1&2\\3&4\end{pmatrix}\) and \(T(v)=(5,11)\). What is \(v\)?
Choose one option.
Show answer
- B. \((1,\,2)\)
Explanation
Look for \(v=(a,b)\) with \(a+2b=5\) and \(3a+4b=11\), which gives \(a=1\), \(b=2\). Check: \(T(2,1)=(4,10)\), which does not match.
Review the concept: Matrix of a linear transformation
The matrix \([T]\) of a linear transformation \(T\), with respect to given bases, has as columns the images of the domain basis vectors, written in coordinates of the codomain basis.
\[[T(v)]=[T]\,[v]\]
More practice problems: matrix of a linear transformation
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