Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: Explain why S is not a basis for R2.S = {(−3, 2)}

A: We know the definition of basis, let V be a vector space. Let B be a set of vectors in vector space…

Q: Let S = {1+ 5x, 1 – 2x-}. Which of the following polynomials could be added to the set S to form a…

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Q: Describe geometrically (line, plane, or all of R 3) all linear combinations of (a) [ 1/2/3 ] and […

A: We know that a set of vectors u1, u2, ……, un is said to be linearly independent if the equation…

Q: Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. P,…

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Q: Do the polynomials x2 + 1, x? – 1, 2x – 1 form a basis in P2

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Q: Which of the following is a basis for R? O a. {(1,0), (2,0)} O b. (1,2), (2,3), (1,7)} O c.…

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Q: The set B = {2 – 4x?, 8+ 3x – 16x2, 21 + 9x – 40x²} is a basis for P2. Find the coordinates of p(x)…

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Q: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

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Q: The set of polynomials {1, x² + 3x“, 2x² – 7x4} is a linearly independent set in P4.

A: NOTE: Due to time limit answer of 1 is given here, for other please ask in a different question.…

Q: Explain why S is not a basis for R2.S = {(6, −5), (12, −10)}

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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Q: Determine whether S = {1– x, 2x - 3x2,x2 - 2x3,2 + x3} is a basis for P3

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Q: Explain why S is not a basis for P₂. S = {1x, 1x², −1 − 5x + 6x²} OS is linearly dependent. OS does…

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Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

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Q: Explain why S is not a basis for P2. S = {1 - x, 1 - x², -1 - 4x + 5x2} O sis linearly dependent. O…

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Q: asis: The set B = {2-3x², 8+x-12x², 33x² - (21+ 2x)} is a basis for P₂. Find the coordinates of p(x)…

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} O S is linearly dependent. O…

A: Consider the given functions. S=1-x,1-x2,-1-4x+5x2 Let S is linearly independent and there exist…

Q: Discovery 4.6. Consider 1 -3 -1 A = 1 3 %3D -2 2 3 -1 -2. Compute the product AX by considering X as…

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Q: - --- Let B = Is Ba basis ofR ? Justify and x = %3D 2 3 3 your answer. If yes, compute xR [x]

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Q: 1 Determine whether B= {1-3²,2+t-5t².1+2t} is a basis for P2-

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Q: x-3x+1 7. Is the set {(1,2,-1,3), (1, -1, 2, 0), (-2, 0, 6, 6)} a basis for R¹? Justify your an-…

A: The objective of this question is to determine whether the given set of vectors forms a basis for…

Q: Show that the polynomials P1 = 1+x + x² P2 = x + x² P3 = x2 form a basis for P2.

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Q: s = (6 4 1) (3 −5 1) (8 13 6) (0 6 9) explain why S is not a basis for R3

A: Given S=6,4,1,3,−5,1,8,13,6,0,6,9. We have to explain why S is not basis of R3. Definition:- The…

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.