Consider four vectors v1 = [1,1,1,1], v2 = [-1,0,1,2], v3 =
[a,1,0,b], and v4 = [3,2,a+b,0],...
Consider four vectors v1 = [1,1,1,1], v2 = [-1,0,1,2], v3 =
[a,1,0,b], and v4 = [3,2,a+b,0], where a and b are parameters. Find
all conditions on the values of a and b (if any) for which:
1. The number of linearly independent vectors in this collection
is 1.
2. The number of linearly independent vectors in this collection
is 2.
3. The number of linearly independent vectors in this collection
is 3.
4. The number of linearly independent vectors in...
3. (a) (2 marks) Consider R 3 over R. Show that the vectors (1,
2, 3)...
3. (a) Consider R 3 over R. Show that the vectors (1,
2, 3) and (3, 2, 1) are linearly independent. Explain why they do
not form a basis for R 3 .
(b) Consider R 2 over R. Show that the vectors (1, 2),
(1, 3) and (1, 4) span R 2 . Explain why they do not form a basis
for R 2 .
Topic: Math - Linear Algebra
Focus: Matrices, Linear Independence and Linear Dependence
Consider four vectors v1...
Topic: Math - Linear Algebra
Focus: Matrices, Linear Independence and Linear Dependence
Consider four vectors v1 = [1,1,1,1], v2 = [-1,0,1,2], v3 =
[a,1,0,b], and v4 = [3,2,a+b,0], where a and b are parameters. Find
all conditions on the values of a and b (if any) for which:
1. The number of linearly independent vectors in this collection
is 1.
2. The number of linearly independent vectors in this collection
is 2.
3. The number of linearly independent vectors in...
Find a subset of the given vectors that form a basis for the
space spanned by...
Find a subset of the given vectors that form a basis for the
space spanned by the vectors. Verify that the vectors you chose
form a basis by showing linear independence and span: v1
(1,3,-2), v2 (2,1,4), v3(3,-6,18),
v4(0,1,-1), v5(-2,1-,-6)
Consider the relation on {1,2,3,4} defined by r = { (a, b) :
a > b...
Consider the relation on {1,2,3,4} defined by r = { (a, b) :
a > b } and s = { ( a, b ) : a − b = 1 }. List all elements
of rs
two vectors equal⟨1,−3,−2⟩andv=⟨−2,−1,−1⟩determineaplanein
space. Without using linear algebra and or row reduction, determine
whether the following...
two vectors equal⟨1,−3,−2⟩andv=⟨−2,−1,−1⟩determineaplanein
space. Without using linear algebra and or row reduction, determine
whether the following vectors lie in the plane formed by u and
v.
A. ⟨8, 4, 4⟩
B. ⟨1, 3, −1⟩
C. ⟨6, −4, −2⟩
Do the vectors v1 = 1 2 3 ,
v2 = ...
Do the vectors v1 = 1 2 3 ,
v2 = √ 3 √ 3 √ 3 ,
v3 √ 3 √ 5 √ 7 ,
v4 = 1 0 0 form a basis for R 3 ? Why or why not?
(b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and
a2, where a1 = ...