F(p), then prove that

Q: aslal. llal-1b||<la + b| < lal + |b|

A: Remark: We know that the absolute value (or modulus) | x | of a real number x is defined as the…

Q: Theorem 9.6.4 The function V(x, v) = ar + bxy + cy is positive definite if, and only if, a> 0 and…

A: We have to show that the function Vx, y=ax2+bxy+cy2 is positive definite if and only if a&gt;0 and…

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A:

Q: Prove: If a &gt; 0, then (1/a) &gt; 0.

A: It is given that a&gt; 0.It is known that if ab &gt; 0 then a &gt; 0 or b &gt; 0 or a&lt; 0 or b…

Q: Prove that: (5a + 6b|a, b = Z} = Z

A: To prove that .Concepts used:Consider two sets  and . To prove that , we first need to show and…

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A:

Q: Prove that, there is no simple grcup of order 200.

A:

Q: The system x' = 4y + 10x² - 39x + 34, y' = 4xy + 3x - 14, has a critical point at (2, 1). The change…

A:

Q: best Rank 2 approximation F ind weth respect to I|F|l the where to A -1 2 -1

A:

Q: Find t and P value

A: The given hypothesis is H0:μ=69 versus Ha:μ≠69.

Q: Prove this theorem.

A:

Q: Q31 a) Prove that Re(iz) = -Im(Z)

A:

Q: Find the Re and Im parts of exp(z?)

A:

Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

A:

Q: f(x) (4) lim x-c g(x) L M provided M0 and g(x) #0 for any a E

A:

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: Show that for any positive integers i and j with i > j, we have T;(x)T;(x) = [Ti+;(x) +T;-j(x)].

A: we have to show, for any positive integers i and j with i&gt;j TixTjx=12Ti+jx+Ti-jx Now, we know…

Q: Consider the system below. * = rx + y – x³ jy = -x + ry – 2y Chis system has a fixed point at (0,0).…

A: First we will calculate Jacobian matrix at the origin and then its eigenvalues. Then depending on…

Q: Q3: Prove that i) Intersection is distributive over union for arbitrary number of sets. ii) Union is…

A:

Q: Prove that (b − proja (b)) · a = 0.

A:

Q: Prove that (R x Q) N (Q × R) = Q x Q

A:

Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

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Q: Ε[βο] = βι

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Q: Prove that Σ(;) = 0.

A:

Q: 7.2.9 Additivity Theorem Let f := [a,b] → R and let ce (a, b). Then f E R[a, b] if and only if its…

A:

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

A:

Q: Prove this theorem.

A: First Isomorphism theorem for Rings: Let ϕ be a ring homomorphism from R to S. Then the mapping…

Q: Prove that if A C R and t > 0, then |A| = |AN(-t,t)|+|AN (R\(-t,t))|-

A: