Final answer:
To find the vector x whose image under the linear transformation T is b, we need to solve the equation Ax=b. The vector x is not unique as there can be multiple solutions to the equation Ax=b.
Step-by-step explanation:
To find the vector x whose image under the linear transformation T is b, we need to solve the equation Ax=b.
Given A=⎡⎣⎢10−211−1−215⎤⎦⎥ and b=⎡⎣⎢3−1−7⎤⎦⎥, we have:
⎡⎣⎢10−211−1−215⎤⎦⎥ ⎡⎣⎢x_1x_2⎤⎦⎥ = ⎡⎣⎢3−1−7⎤⎦⎥
Multiplying both sides by the inverse of A:
⎡⎣⎢10−211−1−215⎤⎦⎥-1 ⎡⎣⎢10−211−1−215⎤⎦⎥ ⎡⎣⎢x_1x_2⎤⎦⎥ = ⎡⎣⎢10−211−1−215⎤⎦⎥-1 ⎡⎣⎢3−1−7⎤⎦⎥
Finally, we can determine the values of x by evaluating the resulting expression.
The vector x is not unique as there can be multiple solutions to the equation Ax=b.