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

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: Define vectors v = 3i - 2j and w = -2i + 4j. Blank 1: Find w - v. Blank 2: Find ||2v+w|l.

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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: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: Find Vectors and Perform Vector Operations in R³ Let à = i + 27 + 3k. Find ||a||.

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Q: These are vectors. For all of them, use proper notation and clearly show each step of your work.…

A: Given: P1, 2, 0, Q4, 6, 0, and R6, 14, 0. We have to plot these points.

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

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Q: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

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Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

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Q: Suppose that the vectors [1, –3, 1] and [2, 4, –1] form the sides of a parallelogram. Find the…

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A: If vectors are linearly dependent then they can be expressed as a linear combination of each other

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A: If vectors are parallel then cross product will be zero check they parallel or not

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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: Consider the set V = R − {2}, that is, the set of all real numbers except 2. Define “addition” as…

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Q: Find a vector orthogonal to both = 10 2 and w = 2

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Q: Describe the additive inverse of a vector in the vector space.R3

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Q: Describe the zero vector (the additive identity) of the vector space. R³ X

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Q: a) Use the dot product to verify the type of angle connecting the vectors and y (acute, right or…

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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: Write the interpretation of independent vectors, span, basis and dimension. Take the example of…

A: We have to give the interpretation of independent vectors, span, basis and dimension by taking the…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: [1 -1 5. Find a vector x + 0 such that 2 | 1 4 = 0. -1] 3 x = 8 1 2 6. Solve for x: 2 2 5 x = 3 07

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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.