Determine if (f1, f2, f3, f4, f8) is a basis of R4[x].

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

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

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

Q: 1) Consider the basis V = (e₁, e₁+ e2, e2+ e3, e3+ e4) of F4. Find the dual basis V

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Q: | Let v₁ = (1, −1, 1, − 2), v₂ − (−1, 2, −1, 1), v, −(−2, 1, −1, 5). Determine whether {V₁, V₂, V3}…

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Q: Let p1,P2, P3 € P2 be defined by p1(t) = 2+t+t2, p2(t) = 2 – t+ 3t2, and p3(t) = 10+t+9t². Determine…

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Q: If [a11 a12 A = a21 and B = a22 [b11 b12 b21 b22] are arbitrary vectors in Rx2, then the mapping (A,…

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Q: Explain why S is not a basis for P2. S = {1, 7x, -6 + x², 2x} O sis linearly dependent. O s does not…

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Q: Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the…

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

A: Given a set S={1-x, 1-x2, -1-4x+5x2}  To Explain why S is not a basis for P2.

Q: Explain why S is not a basis for P2. S = {1, 6x, –9 + x², 7x} O Sis linearly dependent. O S does not…

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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: Consider the basis B3 = (x² - 1, x, 1) of P2 (R). Find [2x² + 3x − 5] B (2,3,-5) (2,3,-3) (3,2,-5)…

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Q: Let [3³] Ai B , where B = {b₁,b₂} is a basis in R². Then 3 B 061+06₂

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 3x + 4x²} O s is linearly dependent. O…

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Q: Let v = 3 2. 2. What is the smallest positive

A: Given vectors are: v1=1122 ; v2=1232 ; v3=2134 ; u=321x We have to find the smallest positive…

Q: Explain why S is not a basis for M2,2- $-{::::)) OS is linearly dependent. S does not span M2,2- OS…

A: Given: S=0110, 1001 and M2,2. We have to explain why S is not a basis of M2,2.

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: Show that the set {(1, 2, 1), (2, 1, 0), (1, -1, 2) for a basis for V3(R).

A: We have set of 3-tupples { (1,2,1),(2,1,0),(1,-1,2) }

Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x², 8x} S is linearly dependent. O s does not…

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Q: Determine whether the set S = {4 – t, t³, 6t2, 3t + t³, –1+ 4t} is a basis for P3. Justify your…

A: We need to determine whether the set S={4-t, t3, 6t2, 3t+t3, -1+4t}

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.