MATH221 April 2010
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q9 • Q10 • Q11 • Q12 (a) • Q12 (b) •
Question 02 (c)
Let , ,
(c) Find a vector orthogonal to all of .
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To find a vector orthogonal to all of , we must find a vector whose dot product with each of is 0. Similar to part (b), we can arrange in a matrix.
To find the vector we are looking for, we can solve for the null space of the transpose of . This will satisfy the constraint that the dot product of the vector and each of is 0.
So we solve:
This gives us: