If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A = egin{bmatrix} 1 & -5 & -10 \ -3 & 6 & 3 end{bmatrix} and b = egin{bmatrix} -3 \ 0 end{bmatrix} Find a single vector x whose image under T is b. x = oxed{} Is the vector x found in the previous step unique? A. No, because there is a free variable in the system of equations. B. No, because there are no free variables in the system of equations. C. Yes, because there are no free variables in the system of equations. D. Yes, because there is a free variable in the system of equations.
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Step 1: Set up the equation \( T(x) = Ax = b \) Given \( A = \begin{bmatrix} 1 & -5 & -10 \\ -3 & 6 & 3 \end{bmatrix} \) and \( b = \begin{bmatrix} -3 \\ 0 \end{bmatrix} \), we need to solve the equation \( Ax = b \). Show more…
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