1. Consider the vectors (2,-3, 1), (-1,7,-3), and (8,-1,-1). (a) Find a basis for the span of these vectors showing a row reduced matrix to support your result. State the dimension of this subspace of R. (b) Show that these three vectors are dependent by writing an explicit nontrivial linear combination of these vectons that is the zero vector.

Q: -2 A = -2 1 -1 a. A basis for the column space of A is { }. You should be able to explain and…

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Q: Show that the vectors are orthogonal.

A: Given vectors are u=<u1, u2>=<4, -1>v=<v1, v2>=<2, 8>

Q: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: Prove that the vectors (1,1,0),(3,1,3) and (5,3,3)  are linearly dependent

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Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Let v1=( 0 1 -1 2)^T v2=(1 0 -2 1)^T Let V=Span{v1,v2} Find a basis for the orthogonal complement of…

A: Orthogonal complement : Let V be a vector space in ℝn. The orthogonal complement is the subspace…

Q: Suppose V is a subspace of R" and suppose {v1, v2, v3} is a basis of V. Decide if the following sets…

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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.