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(Solved): Problem 2. Find the standard matrix for the matrix operator defined by the equation and determine wh ...
Problem 2. Find the standard matrix for the matrix operator defined by the equation and determine whether
the operator is one-to-one.
w_(1)=x_(1)+2x_(2)-x_(3)
w_(2)=x_(1)-4x_(2)+x_(3)
w_(3)=x_(1)-3x_(2)+x_(3)
[10 marks]
Problem 3. Find T^(-1)(w_(1),w_(2),w_(3)) for a given matrix
w_(1)=x_(1)+2x_(2)+x_(3)
w_(2)=-2x_(1)+x_(2)+4x_(3)
w_(3)=7x_(1)+4x_(2)-5x_(3)
[10 marks]
Problem 4. Let T_(A):R^(3)->R^(3) be multiplication by
A=[[4,-1,0],[1,3,1],[-1,1,4]]
and let e_(1),e_(2), and e_(3) be the standard basis vectors for R^(3).
Find the following:
(a) T_(A)(e_(1)),T_(A)(e_(2)),T_(A)(3e_(3)),
(b) T_(A)(e_(1)+e_(2)+e_(3)).
[10 marks]