1.

The standard ordered basis of R3 is {e1, e2, e3} Let T : R3 → R3 be the linear transformation such that T(e1) = 7e1 - 5e3, T (e2) = -2e2 + 9e3, T(e3) = e1 + e2 + e3. The standard matrix of T is:

A. \(\left( {\begin{array}{*{20}{c}} 7&0&1\\ 0&{ - 2}&1\\ { - 5}&9&1 \end{array}} \right)\)
B. \(\left( {\begin{array}{*{20}{c}} 7&-2&1\\ -5&{ 9}&1\\ { 0}&0&1 \end{array}} \right)\)
C. \(\left( {\begin{array}{*{20}{c}} 7&0&-5\\ 0&{ - 2}&9\\ 1&1&1 \end{array}} \right)\)
D. \(\left( {\begin{array}{*{20}{c}} 7&-5&0\\ -2&{ 9}&1\\ { 1}&1&1 \end{array}} \right)\)
Answer» B. \(\left( {\begin{array}{*{20}{c}} 7&-2&1\\ -5&{ 9}&1\\ { 0}&0&1 \end{array}} \right)\)


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