Suppose that ( T ) is a linear transformation such that [ Tleft(left[egin{array}{c} 2 \ -1 end{array} ight] ight)=left[egin{array}{c} 5 \ 11 end{array} ight], quad Tleft(left[egin{array}{c} -4 \ -3 end{array} ight] ight)=left[egin{array}{c} 15 \ -7 end{array} ight], ] Write ( T ) as a matrix transformation. For any ( vec{v} in mathbb{R}^{2} ), the linear transformation ( T ) is given by ( T(vec{v})= )
Added by Joel W.
Close
Step 1
Since \( T \) is a transformation from \( \mathbb{R}^2 \) to \( \mathbb{R}^2 \), \( A \) will be a 2x2 matrix. We can write \( A \) as: \[ A = \left[\begin{array}{cc} a & b \\ c & d \end{array}\right] \] Step 2: We are given that \( T \) transforms the vector \( Show more…
Show all steps
Your feedback will help us improve your experience
Danielle Fairburn and 96 other Linear Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Recommended Videos
Oswaldo J.
Assume that $T$ defines a linear transformation and use the given information to find the matrix of $T.$ $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{4}$ such that $T(-1,1)=(1,0,-2,2)$ and $T(1,2)=(-3,1,1,1).$
Linear Transformations
Definition of a Linear Transformation
Suppose that T is a linear transformation such that T ([1 -1]^T) = [-5 9]^T, T ([-3 -2]^T) = [5 -7]^T, Write T as a matrix transformation. For any v ∈ R^2, the linear transformation T is given by T(v) = [-7 -2; 5 -4] v.
Recommended Textbooks
Linear Algebra and Its Applications
Differential Equations and Linear Algebra
Elementary Linear Algebra: Applications Version
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD