Let P3 be the vector space of all polynomials of degree 3 or less in the variable z. Let 2 - z+z? - r', 6 – 3z + 3r? - 3z, 2+z? - z, P1(z) %3D P2(z) P3(z) P:(z) %3D 3 -z+ 2z? - 2z³ %3!

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

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Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: Determine the interpolating polynomial in Newton's form that passes through the points and Use the…

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Q: Find a polynomial y = p(x) of degree 4 that goes through the points (0, 4), (1, 2), (2, -4), (3,…

A: solution of the given question is like this:

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

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Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: EXER 3.2 - LINEAR ALGEBRA Write v =(4,4,5) as a linear combination of x=(1,2,3), y =(-2,0,1) and z =…

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Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

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Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

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Q: Use the function to find the image of v and the preimage of w. T(V,, V2, V3) = (4v, - v,, 4v, +…

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Q: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

Q: Find the length of the projection of [−8 −7]onto the vector [−7 5]   Its written vertically…

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Q: Show how v is orthogonal to any linear combination formed by w1 and w2

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Q: Write x3 + 2x + 1 as a product of linear polynomials over some extension field of Z3.

A: Given: x3+2x+1. To Do:We have to write x3+2x+1 as a product of linear polynomials over some…

Q: If a, and b are non - collinear vector and vectors a = (x +4 y)a +(2x + y +1)b and, B= (-2x + y + 2…

A: We will solve the following

Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

A: Two vectors are said to be orthogonal if their dot product is zero. Dot Product There are two…

Q: = If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V₂ W₁ +W2 independent or…

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Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: T: P2 P₂ defined by T(a + bx + cx2) = a + b(x + 8) + b(x + 8)² Find the following images of the…

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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.