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MAT2611 ASSIGNMENT 9 2023
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MAT2611 ASSIGNMENT 9 2023. 100% CORRECT questions, answers, workings and explanations. for assistance.
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MAT2611 ASSIGNMENT 9 2023, ASSIGNMENT 09
Due date: Friday, 11 August 2023
Problem 31. Suppose S = fv1; v2g is a basis of R2; where v1 = (1; 1) and
v2 = (2; 0).Let T : R 2 ! R 2 be the linear operator for which
T (v1) = (3; 2) and T (v
2) = ( 1; 0) :
Find a formula for T (x; y) ; and compute T (3;
2).
[25 marks]
Problem 32. Let T be multiplication by the matrix
2 3
2 0 1
A=4 4 0 25
20 0 0
1. Find a basis for the range of T .
2. Find a basis for the kernel of T .
3. Find the rank and nullity of T .
4. Find the rank and nullity of A.
[25 marks]
Problem 33. Let A be a 4 6 matrix with rank 3.
(1) What is the dimension of the solution space of Ax = 0.
(2) Is Ax = b consistent for all vectors b in4?RExplain.
[25 marks]
Problem 34. Let v1; v2; and v3 be vectors in a vector space V; and let
T : V ! R 3 be a linear transformation for which
T (v1) = (1; 3; 2) ; T (v2) = (0; 1; 3) ; T (v3) = ( 1; 2; 1) :
Find T (2v1 v2 + 3v3).
[25 marks]
[Total:100 marks]
–End of assignment –
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