Exercise · ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-002 · ★☆☆ Basic
Let \(T:\mathbb{R}^3\to\mathbb{R}^2\) be linear. What size is its matrix in the standard bases?
Choose one option.
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- C. \(2\times3\)
Explanation
It has one column for each vector of the domain basis (3) and one row for each coordinate of the codomain (2): it is \(2\times3\).
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?
- ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-008 The derivative D acts on polynomials of degree at most 2. What is its matrix in the basis \1, x, x^…
- ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-009 The matrix of T in the standard bases is [1 2; 3 4] and T(v)=(5,11). What is v?
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