Find the dimensions of the following vector spaces. (a) The vector space R5 (b) The vector space M6×7 (c) The vector space of 2 × 2 matrices with trace 0 (d) The vector space P3 of polynomials with degree less than or equal to 3 (e) The vector space of all diagonal 2 × 2 matrices (f) The vector space of all lower triangular 4 × 4 matrices Find a basis {p(x), q(x)} for the vector space {f(x) = P2 | ƒ'(−8) = f(1)} where P₂ is the vector space of polynomials in x with degree less than or equal to 2. p(x) = ☐, q(x) = = 0

Q: Find a basis of the subspace of R* defined by the equation 5x1 - 7x2+8x3 6х4 = 0. 9. 9. 9. Basis: 9.…

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Q: S[y] given by y = cosh æ + B sinhx, 0 0,

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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: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

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Q: 3 a) We defined span and looked at the span of a set of vectors geometrically and numerically…

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Q: -9 -10 12 -15 A = 4 -8 6 6 0 9

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Q: Does the set of all 2x2 matrices form a vector space, please explain.

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Q: Describe the zero vector (the additive identity) of the vector space. P3 x + ]+² +

A: We have to describe the zero vector (the additive identity ) of the vector space P3.

Q: w that the space V = {(x1, x2, x3) ∈F3

A: To prove that the space V=(x1, x2, x3)∈F3|x1+2x2+2x3=0 forms a vector space.

Q: Find bases for the row space, column space and null space of 2 1 3 4 A: = 1 1 2 4 2 4 2 37 68

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Q: Find a basis for the column space of -2 4 4 A = 3 3 4 -2 -16 -8

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Q: 1-What is the definition of the characteristic polynomial of a square matrix A?

A: Here, we have to define characteristic polynomial of a square matrix.