Find the matrix representation of the linear transformation T that maps the input vector x→1=(1,1)T to the output vector y→1=(2,−3)T and maps the input vector x→2=(1,2)T to the output vector y→2=(5,1)T

Step 1 Suppose the matrix is V, then we have [x1x2]V=[1112]V=[25−31]=[y1y2] Consider to find the inverse matrix of [x1x2]

Step 1 You can write this as a matrix equation. Create a matrix X from x→1 and x→2, and another one Y from y→1 and y→2. Then TX=Y. Multiply both sides on the right with X−1 and you get the answer. T=(25−31)(1112)−1

Step 1 Suppose the matrix is V, then we have [x1x2]V=[1112]V=[25−31]=[y1y2] Consider to find the inverse matrix of [x1x2]

Step 1 You can write this as a matrix equation. Create a matrix X from x→1 and x→2, and another one Y from y→1 and y→2. Then TX=Y. Multiply both sides on the right with X−1 and you get the answer. T=(25−31)(1112)−1

Best solutions to - "Find the matrix representation of the linear transformation..."

College
Algebra
Linear algebra
Matrix transformations

Emerson Barnes

Answered question

2022-02-01

Find the matrix representation of the linear transformation T that maps the input vector

{\vec{x}}_{1} = {(1, 1)}^{T}

to the output vector

{\vec{y}}_{1} = {(2, - 3)}^{T}

and maps the input vector

{\vec{x}}_{2} = {(1, 2)}^{T}

to the output vector

{\vec{y}}_{2} = {(5, 1)}^{T}

Answer & Explanation

Ydaxq

Beginner2022-02-02Added 12 answers

Step 1
Suppose the matrix is V, then we have

[\begin{matrix} x_{1} & x_{2} \end{matrix}] V = [\begin{matrix} 1 & 1 \\ 1 & 2 \end{matrix}] V = [\begin{matrix} 2 & 5 \\ - 3 & 1 \end{matrix}] = [\begin{matrix} y_{1} & y_{2} \end{matrix}]

Consider to find the inverse matrix of

[\begin{matrix} x_{1} & x_{2} \end{matrix}]

stamptsk

Beginner2022-02-03Added 23 answers

Step 1
You can write this as a matrix equation. Create a matrix X from

{\vec{x}}_{1}

and

{\vec{x}}_{2}

, and another one Y from

{\vec{y}}_{1}

and

{\vec{y}}_{2}

. Then

T X = Y

. Multiply both sides on the right with

X^{- 1}

and you get the answer.

T = (\begin{matrix} 2 & 5 \\ - 3 & 1 \end{matrix}) {(\begin{matrix} 1 & 1 \\ 1 & 2 \end{matrix})}^{- 1}

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