6) We defined span and looked at the span of a set of vectors geometrically and numerically working with vectors from Rn. When a set of vectors spans a space the linear combination of them generates every object in the space.  Can you think of a set of 2x2 matrices such that when you take the span of them you can generate any 2x2 matrix? (hint: think of our standard basis for R2, R3, ... etc.)

Q: Assume that T is a linear transformation. T: Projects vectors in its domain onto the line y = 2/3 x.…

A:

Q: 19. Can each vector in R4 be written as a linear combination of the columns of the matrix A above?…

A:

Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

A:

Q: Let A be a m x n matrix whose columns are vectors of R™. What is the smallest n must be so that…

A: Let A be the m×n matrix A=a11a12…a1na21a22…a2n⋮⋮⋱⋮am1am2…amnm×n that is the transformation matrix…

Q: Find a non-zero vector in Nul A and a non-zero vector in Col A for the following matrix: 1 2 3 4 5 7…

A: We will first find a basis for Nul A and Col A then we will find the required vectors.

Q: 4. Describe all matrices row equivalent to the matrix: [B]

A: Since you have posted a multiple question according to guildlines I will solve first(Q4)   question…

Q: 8. Let V be the set of all 2 x 2 matrices with the standard componentwise definitions for vector…

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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.