0
(i) They are linearly dependent since the 2nd vector is twice the 1st vector.
All 3 vectors lie in the x-z plane, so they don't span 3D space.
(ii) They are linearly independent.
Note that the cross-product of the first two is (-1,1,1).
If the third vector is not perpendicular to the above cross-product,
then the third vector does not lie in the plane defined by the first two vectors.
(-1,1,1) "dot" (1,1,-1) = -1+1-1 = -1, not zero, so 3rd vector is not perpendicular
to the cross product of the other two.
What else can I help you with?
If a set of vectors spans R3 then the set is linearly independent?
No it is not. It's possible to have to have a set of vectors that are linearly dependent but still Span R^3. Same holds true for reverse. Linear Independence does not guarantee Span R^3. IF both conditions are met then that set of vectors is called the Basis for R^3. So, for a set of vectors, S, to be a Basis it must be:(1) Linearly Independent(2) Span S = R^3.This means that both conditions are independent.
Most problems can be solved by following what?
set of steps
Which of the following describes something that is quantized?
It has a specific set of possible values.
Each Firewall Rule provides a set of conditions that which of the following has to meet?
Traffic
Why is the set of even counting numbers well defined?
Because the description which is given is sufficient to decide whether or not any given number is in the set.
How do you prove that set A of vowel is a subset of set B that is equals a letter that appear in a girl's name?
To check whether a set is a subset of another set, you check whether every element of the first set is also an element of the second set.
Is weight and displacement a set of vectors?
No, weight and displacement is not a set of vectors. A vector in the area of mathematics is defined as a direction as well as a magnitude of a specific item. Vectors can be labeled in a variety of ways.
If a set of vectors spans R3 then the set is linearly independent?
No it is not. It's possible to have to have a set of vectors that are linearly dependent but still Span R^3. Same holds true for reverse. Linear Independence does not guarantee Span R^3. IF both conditions are met then that set of vectors is called the Basis for R^3. So, for a set of vectors, S, to be a Basis it must be:(1) Linearly Independent(2) Span S = R^3.This means that both conditions are independent.
What is Linearly independent Vectors?
Linearly independent vectors are a set of vectors in which no vector can be expressed as a linear combination of the others. This means that the only solution to the equation formed by setting a linear combination of these vectors to zero is that all coefficients must be zero. In other words, if you have a collection of linearly independent vectors, removing any one of them would alter the span of the set. This concept is fundamental in linear algebra, particularly in determining the dimensionality of vector spaces.
How to find orthogonal vector?
Given one vector a, any vector that satisfies a.b=0 is orthogonal to it. That is a set of vectors defining a plane orthogonal to the original vector.The set of vectors defines a plane to which the original vector a is the 'normal'.
The resultant of a set of vectors is?
The single vector which would have the same effect as all of them together
How is a resolution of a vector different from the resultant of vectors?
When you resolve a vector, you replace it with two component vectors, usually at right angles to each other. The resultant is a single vector which has the same effect as a set of vectors. In a sense, resolution and resultant are like opposites.
What is vector plane?
A vector plane is a two-dimensional space defined by a set of two non-parallel vectors. It represents all linear combinations of these vectors. In linear algebra, vector planes are used to visualize and understand relationships between vectors in space.
If a set of vectors is laid head to tail and formed a closed polygon is the resultant zero?
yes it is
Gram schmidt matlab code for orthonormalizing set of vectors?
gram schmidt matlab code
What is an independent system of linear equations?
An independent system of linear equations is a set of vectors in Rm, where any other vector in Rm can be written as a linear combination of all of the vectors in the set. The vector equation and the matrix equation can only have the trivial solution (x=0).
What is independent linearity?
Independent linearity refers to a property in linear algebra related to the linear independence of vectors in a vector space. A set of vectors is said to be linearly independent if no vector in the set can be expressed as a linear combination of the others. In terms of independent linearity, it implies that the vectors maintain their distinct contributions to the span of the space they occupy, ensuring that the maximum number of linearly independent vectors corresponds to the dimension of the space. This concept is crucial for understanding the structure and dimensionality of vector spaces.
