= (-)e, + x,2e, satisfies the conditions of the inverse function theorem for 7.51. Show that f(x) all x except * = 0 but is not 1-1 on this set. ohos olo tgeono 8 Show that the function

Q: When the vector b = -2 is projected onto the line spanned by the vector a = 1 what is the error 2…

A: The projection of b onto a line spanned by a vector a is  b.a^=b.a|a| Given:  b=[-2-2-1]…

Q: What is a vector?

A: A quantity that has magnitude as well as direction is called a vector.

Q: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

A: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

Q: 'S' is a collection of vectors. Show that the rank of S is equal to the dimension of Span(S). Please…

A: Let  is a collection of vectors. Now, let the rank of is equal to  (say).It's row reduced eschelon…

Q: What is the least number of linearly independent vectors needed to span a line? [Enter a whole…

A:

Q: what are the examples of contravarient and covariant tensors?

A: Example of Covariant tensor: A'i=aijAj

Q: Explain why there is no vector v such that × v =.

A: We explain why there is no vector v such that  <1,2,1> × v =<3,1,5>

Q: Define direction vector.

A: Define direction vector.

Q: Why is HE vector twice of vector V?

A:

Q: Explain the term scalar.

A: Explanation: Given that, term scalar.

Q: We know that there are two ways to multiply vectors: the vector and scalar product. How about vector…

A: Vector division is not possible .

Q: Which of the following vectors is opposite of the given vector below?

A:

Q: Find  vector z + vector y if vector z= and vector y= . graph

A:

Q: discuss the directional vectors (gradient and curl) with physical examples.

A:

Q: Compare between zero vector and unit vectors with drawing the suitable curves.

A: Solution : Here we have show the difference between the Zero vector and Unit vector.   Concept : A…

Q: write the general solution to  x+y+z+w=1 x+y-z-w=1 as a vector in the form of y or w

A: NOTE: Refresh your page if you can't see any equations. . the system Ax=b is

Q: How can we find the cartesian equation from a vector equation?

A: Equation of line in vector form is:r→=a→+λb→Where,a→=x1i→+y1j→+z1k→ b→=b1i→+b2j→+b3k→

Q: Define the gradient vector, and explain what it means. Come up with an example you're your own life,…

A: To find- Define the gradient vector and explain what it means. Come up with an example you're your…

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: what if it was the same vector, but 5y^2j?

A:

Q: What role does the curl of a vector play in an application?

A: We have to write the curl of a vector play in an application.

Q: Write out the expressions a- Va in index notation for vector a

A: Let us consider a vectora→ = a1i^ +a2j^ +a3k^where a1 , a2, a3 are functions of (x1, x2 & x3)and…

Q: what is Scalar variable ?

A: A scalar variable is used for storing a value that has no internal component. The value may change.…

Q: Identify the type of answer that results from each operation (vector or scalar). If the operation is…

A:

Q: Explain how to find the unit vector in the direction of any given vector v.

A: To find the unit vector in the direction of the given vector v, divide the vector v by its…

Q: 4. Find two vectors and such that (i) both and are perpendicular to = (1,0,-1) and (ii) is…

A:

Q: 1 If vector is a unit vector, what is the x?

A: We will find the value of x as following.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.