Consider the vector space R 4 over the field of real numbers F = R 4. Let W = { ha, b, c, di | where a - 2d = 0 and a, b, c, d are real numbers } Show that W is a subspace of R * .

Q: 6. Let Vi and V2 be subspaces of R" such that Vi C V2. Show that any vector v E R" can be uniquely…

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Q: Consider the vector v = (6, 1, -3) in R. Let V be the subspace of R consisting of all vectors of the…

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Q: Let W be the subspace of R spanned by the vectors -2 and Find the matrix A of the orthogonal…

A: Given that  W be the subspace of ℝ2 spanned by the vectors                           1-21  and…

Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

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Q: Show that the set W={(x,y,1)|x and y are real} is not subspace of R3.

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Q: Does the set of all functions that vanish at x = 0 and x = L form a vector space? If it does,…

A: 1) Commutativity of addition: Let f(x) and g(x) be functions in V.Then, .Therefore, addition is…

Q: Let V be the vector space of polynomials in t of degree ≤ 3. Determine whether the following vectors…

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Q: If W is a subspace of R" and ax is in W, where a is a nonzero scalar and x is in R". Then x is in W/…

A: We have to check

Q: Find a linearly independent collection of vectors which spans the following subspace of R4: 2 3 -3…

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Q: Find the distance from the point x = (1, 5, –4) of R³ to the subspace W consisting of all vectors of…

A: First we will find out the orthogonal basis for the subspace W. Then we calculate the orthogonal…

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.