The standard ordered basis of R 3 is {e 1 , e 2 , e 3 } Let T : R 3 → R 3 be the linear transformation such that T(e 1 ) = 7e 1 - 5e 3 , T (e 2 ) = -2e 2 + 9e 3 , T(e 3 ) = e 1 + e 2 + e 3 . The standard matrix of T is:

Correct Answer is : (7010−21−591)

\left(\begin{array}{ccc}7 & 0 & 1 \ 0 & −2 & 1 \ −5 & 9 & 1 \ )\end{array}

\left(\begin{array}{ccc}7 & −2 & 1 \ −5 & 9 & 1 \ 0 & 0 & 1 \ )\end{array}

\left(\begin{array}{ccc}7 & 0 & −5 \ 0 & −2 & 9 \ 1 & 1 & 1 \ )\end{array}

\left(\begin{array}{ccc}7 & −5 & 0 \ −2 & 9 & 1 \ 1 & 1 & 1 \ )\end{array}

AAI ATC Junior Executive 2018 Shift 1 Paper

Question : 78 of 120

Marks: +1, -0

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:

${(\table 7 , 0 , 1 ; 0 , −2 , 1 ; −5 , 9 , 1 ; )}$
${(\table 7 , −2 , 1 ; −5 , 9 , 1 ; 0 , 0 , 1 ; )}$
${(\table 7 , 0 , −5 ; 0 , −2 , 9 ; 1 , 1 , 1 ; )}$
${(\table 7 , −5 , 0 ; −2 , 9 , 1 ; 1 , 1 , 1 ; )}$

Validate

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