Science:Math Exam Resources/Courses/MATH307/April 2006/Question 05 (d)
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Question 05 (d) 

A matrix A and a vector b are given by
Determine if is solvable. Find x if it is solvable and find x (i.e. the least squares solution) if it is not. 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2006/Question 05 (d)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From part c, we note b is not in R(A) therefore it is not solvable. We will proceed by solving the least squares solution by QR decomposition A=QR from part a
since Q has columns of orthonormal vectors, Q is orthogonal
The solution to our least square problem is
