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: 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: 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…

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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: 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: 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: 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: 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.