Linear Equations in Linear Algebra, Algebra

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Question 1 [7 marks]
The reduced row echelon form of
?
?
?
?
?
?
?
?
?
?
? ?
3
4 17 22
1 2 5
row
a
b
A is equal to
?
?
?
?
?
?
?
?
?
?
? ?
0 0 0 0
0 0 1 2
1 2 0 3
R .
(a) What can you say about row 3 of A? Give an example of a possible third row for A.
(b) Determine the values of a and b.
(c) Determine the solution of the homogeneous system of equations Rx = 0 in parametric vector
form.
(d) What is the dimension of the column space of A? Do the columns of A span R3 ?

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