Exercise · ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-006 · ★★☆ Intermediate
It is known that \(T(1,0)=(1,2)\) and \(T(0,1)=(3,-1)\). What is \(T(2,5)\)?
Choose one option.
Show answer
- C. \((17,\,-1)\)
Explanation
The matrix has columns \((1,2)\) and \((3,-1)\), and \(T(2,5)=2(1,2)+5(3,-1)=(17,-1)\). Swapping the coefficients would give \((11,8)\), which is wrong.
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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- ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-007 S has matrix A=[1 1; 0 1] and T has matrix B=[2 0; 0 3]. What is the matrix of T∘ S?
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