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Linear Transformations - Unique Solutions

Show that the system of equations

2x + y + z = -6a
2x + y + (b +1)z = 4
bx + 3y + 2z = 2a

Has a unique solution except when b = 0 and b = 6.

If b = 0, show that there is only one value for a for which a solution exists, and find the general solution in this case.

Discuss the case when b = 6.

Interpret your solutions in terms of the kernel and image of the linear transformation T: o^3 --> o^3 represented by the equations.

Solution Preview

Let A = (2 1 1) (x) (-6a)
(2 1 b+1), X = (y), B = (4)
(b 3 2) ...

Solution Summary

This shows how to prove that the given system has a unique solution except for certain points in an attached Word document.

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