Example: Matrix Examination

Thursday, 20 June 2019

4:51 PM

Untitled picture.png Machine generated alternative text:
Question 4: Score 1/1
(a) LetP6 be the vector space of all the polynomials of degree 6 or less.
The dimension ofP6 is
e
Your response
7
Grade: 2/20
(b) Let V and S {VI' •
.. , v6} be a set of 6 vectors in V.
Suppose that W span(S) is the subspace of V spanned by S.
IV6) be the matrix with the vectors in S as columns, and b e IR7
Let A (Vil •
The system Ax = b is consistent. That is solution(s) exists.
The system Ax O has infinitely many solutions.
Fill in the following answer fields using drop down menus.
The vector b
Your response
Grade: 1/1.0
in the span of W
The set S is a linearly
Your response
dependent
Grade: 1/1.0
e
t in V.
The dimension of W
Your response
IS less than 6
Grade: 1/1.0
Correct response
Correct response
Correct response
Correct response
e
Ink Drawings

Machine generated alternative text:
The dimension of Mm n is m x n.
The dimension of Pn is n + 1 .
For a vector space V, if S is a finite spanning set for V and T is a linearly independent set in V, then
ITI dim(V) ISI,
where ITI and ISI are the number of elements of T and S, respectively.
A basis for a vector space V is a linearly independent spanning set for V.
The dimension of a vector space V, with a finite spanning set, is the number of vectors in a basis for V.

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