Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 202 05 (c)

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MATH307 April 2013

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Question Section 202 05 (c)
Suppose that A is the following 3 x 4 with $A={\begin{bmatrix}1&1&0&1\\2&2&1&3\\3&3&1&4\end{bmatrix}}\quad \mathrm {rref} (A)={\begin{bmatrix}1&1&0&1\\0&0&1&1\\0&0&0&0\end{bmatrix}}$ (c) Find a basis for R(AT).

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Solution
This is equivalent to the pivot rows of rref(A) since the range or columns space of $A^{T}$ is equal to row space of A. The rows are written as columns. Therefore the basis for R ($A^{T}$) = ${\begin{bmatrix}1\\1\\0\\1\end{bmatrix}}$ and ${\begin{bmatrix}0\\0\\1\\1\end{bmatrix}}$.

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