5. Let v1, V2, ..., Vn € R". Let A be then x n matrix whose j-th column is v; (j = 1, 2, n), that is, A = v2 .. V1 Vn Prove that V1, V2, ..., Vn form a basis for R" det (A) # 0.

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(6, 0), (0, 2)}, x = (48, 10)

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Q: Suppose A is the matrix for T: R3 → R3 relative to the standard basis. Find the diagonal matrix A'…

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Q: Find the coordinate matrix of x in R^ relative to the basis B'. B' = {(5, 0), (0, 2)}, x = (10, 8)…

A: If A is a basis, then x∈Rn can be written as linear combination of the elements of A. When a scalar…

Q: 3. Give an example of an orthonormal set with 4 non-trivial vectors in R5.

A: We have to solve given problem:

Q: Denote the column vectors of the matrix 11,922.. , ann +] True, false, or uncertain: a; is…

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Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

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Q: tind the equation of a polynomial Shose graph, passes through the points t-1,7), (0,2)(2;4)

A: As per guidelines I had solved the first question. Thank you.

Q: 1 3 Let the inner product in R be generated by the matrix 4 = -1 2 Calculate the inner product of…

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Q: 8. Which of the following are orthonormal s 1 A = {U₁ = (₂0₁2), U₂=(2,0, B = { U₁ = (2,0, ₂2), U₂ =…

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Q: Proposition 11.5.1. If A and B are is defined, then matrices such that the matrix product (AB)=BT…

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Q: 1s) La L : A → R be the limsir operator Lip(z)) – p(0)r*+27/(c). Find the matrix A representing with…

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Q: 22. Find a basis for R4 that contains the vectors (3, 2, 3, 3) and (5, 4, 5, 5)

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Q: 10. Let (1,2,3) be a solution for the vector equation ru + yv + zw = 0 and consider the matrix…

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Q: 7) Find the Jacobian matrix at The print (1,2,1) of The Willowing Funchun: soudainish and Nidevorsh…

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Q: 2 COLAS -1 Consider the two bases B= for R² and C= P √2 a.) Compute the change-of-coordinates matrix…

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Q: Let A be a 9x6 matrix with nullify equal to 1 a) find the rank and nullify of A^T  b) suppose that…

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Q: 9. Consider the orthonormal basis S for R³ S = (v₁,v₂,v,} where v₁ = (0,1,0) and v₁ = Let u = V₂ = =…

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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.