Question

Let t be defined as t(x) = ax. Find a vector x whose image under t is b, where a = 1 -3 2 0 1 -4 3 -5 -9 and b = 6 -7 -9?

Answer 1

To find a vector x whose image under the transformation t is b, we need to solve the equation t(x) = b. However, in this case, the given matrix a is not invertible, so there is no vector x that will satisfy the equation.

Step-by-step explanation:

To find a vector x whose image under the transformation t is b, we need to solve the equation t(x) = b. In this case, t(x) = ax, where a is given as 1 -3 2 0 1 -4 3 -5 -9 and b is given as 6 -7 -9.

We can solve for x by multiplying the inverse of a (if it exists) with b. Let's denote the inverse of a as a-1. Then, x = a-1 b. Depending on the dimensions and properties of a, we can find the inverse of it and compute the result.

However, in this case, the given matrix a is not square, which means it is not invertible. Therefore, there is no vector x that will satisfy the equation t(x) = b.