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1. Given
Find each of the following:
Solvability condition
Particular solution for
Complete solution
2. Choose a vector in each of the fundamental spaces of A. Prove that your choice lives in the space the use these to verify the following.
∀b ∈ C(A) ⊥ ∀y ∈ N(AT)
and
∀r ∈ C(AT) ⊥ ∀x ∈ N(A)
3. Identify the independent columns of A. Use the definition of linear independence to prove that the independent columns of A are linearly independent.
4. In the vector space P3 of all p (x) = a0 + a1x + a2x2 + a3x3, let S = {p(x)|p(x)∈P3,p'(0)= 0]. Verify that S is a subspace.
5. Determine if T(v) v except that T(0, v2) = (0,0) is a linear transformation.
6. Prove that two nonzero orthogonal vectors in R2 are linearly independent.
7. What multiple of
is closest to the point b =
8. Find the projection matrix P that projects b onto the line through a.
Verified Expert
paper was combination of Matrix and vectors. Both are inter related. Vectors are very useful in day to day life including mentioning and solving many scientific problems. As vectors show the direction and value of particular object or physical quantity. But sometimes vectors can be complicated in presentation and in description. To find out what will be the output of so many vectors in multi-dimensional space we need the help of Matrices. As properties of Matrices help us to represent or to get the output out of so many vectors to find out the certain properties of vectors. These methods are often used in gaming or designing where certain points of certain objects represent certain vectors regarding reference object and in certain condition how they will react or change that can be sort out by using matrices by filling up these vectors in them.
Savage Inequalities is a wonderful book to reference here as it does point to the problem of inequitable funding. In other words the poor stay poor because the school is funded disproportionally from community to community.
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