3. [6 points] Consider the vector space V = P, over the field of real numbers F = R. Is the vector 4 – x – x² in the span of the vectors %3D 1+ 2x, x – x², -1+x+x² Explain why or why not. Show your calculations.

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

A:

Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: 4 В T(t+h) A 21 y 01 2

A:

Q: Consider the set V of all vectors of the form (x y z)T where x, y and z are real numbers. 3. Show…

A:

Q: The figure shows a rectangular box in three- dimensional space that contains several vectors. (The…

A:

Q: Q11: Let vector v = (-7, 5) and vector w=(2, 2). Write vector v as the sum of two orthogonal…

A:

Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

A:

Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

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Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

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Q: (2) Let vị = ( 2 = (2),v3 1 of the vector space R³. (2a) Does the vector v = (6 belong to…

A: Linearly independent vectors: The set of vectors v1, v2, ..., vn is said to be linearly independent…

Q: be rational numbers. Show that R is a vector space over the rational numbers Q, using standard…

A: We proved all the properties of a vector space.

Q: 7. Find the scalar equation of any plane which contains the line = (1,2,1)+ t(3,6,-1)

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Q: Let vi = (-9,9, 6). v2 = (2, 6, 4). v3 = (4,0,0) in Rº. Find a nontrivial linear relation among…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Distance = 4.41

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

A:

Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: a State the condition(s) that a, b, c, and d must satisfy for the vector b to be 1 1 -1 and spanned…

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Q: Determine whether the vectors ?→ = (2,−1,3), ? → = (1,1,−2), and ? → = (3,−1,5) span ℝ?. If not find…

A: Span: Let us consider the set of  vectors S={v1,v2,v3,......vn} in a vector space V is said to be…

Q: 16. For any vectors a, b and c, show that a. (axb) xc lies in the plane of a and b b. (a x b) X c =…

A: Step 1: Reference: Vector Calculus, Vector triple product

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.