4. Let A = . Show that A can be diagonalised. Then, compute Aº.

Q: 29. Compute det B, where B = 1 2 2

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Q: Let J={a: aER}, then I is Borel algebra.

A: False Statement' Detailed Explanation

Q: Prove that if a, b e Z – {0}, then gcd(a, b) = gcd(a, -b)

A: Solution:-   gcd a,b= Greatest common divisor of  a  and  b ∗Every integer  that divides  a  and  b…

Q: For A ∈ Mn(C) show that A = A1 + iA2 uniquely with A1 and A2 selfadjoint. Show that A is normal if…

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Q: Let i = i +2j+3k , Find e so that ||c|| = 3.

A: As we know that; The property of scalar multiplication of a vector ka→=ka→ Given: u→=i→+2j→+3k→

Q: Let A, BC X. Is Bd(A) C Bd(B)?

A: We want to check for A, B ⊂ X Is Bd(A) ⊂ Bd(B) true or false.

Q: Let A and U = H. Then A2017U is equal to

A: The given matrix is A=-120-1 find A2=-120-1-120-1=1+0-2-201=1-401 therefore A2=1-401 similarly…

Q: Let A = 2 and U = H Then A2017U is equal to A D

A: Given A = -120-1  and  U = 10

Q: If ||u|| = 2, ||v|| =√3 , and u x v = 1, find ||u + v||.

A: Given that u=2,   v=3   and  u*v=1. This implies that,

Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

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Q: Prove that if T+¬AFB and I+¬A¬B, then I EA

A: Given proposition is Γ+¬A-B and Γ+¬A-¬B To prove Γ-A Now,  1. Γ+¬A-B∧Γ+¬A-¬B…

Q: Prove that A CB P(A) C P(B).

A: We have to prove that

Q: Let j = 7 and U=span(ü), with ü = -6. Write j = ã1+ã2, where 1 in U and az in U-.

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Q: Prove that, if (a%m)=(b%m) then m| (a-b)

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Q: Prove that ifx > 3 and y> 4, then xy > 11.

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Q: Given Ā =, B =,č = (a) Compute Ā· (B + T) (b) Compute A · (B × C)

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Q: If i = j+z, i – j = đ, and j – z = b, show that ā = -15.

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Q: 2 Let aj 3 (a) Write b as a linear combination of a and a2.

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Q: Shaa thut the graf of lincs iju fins rom F from E Iwhore is a iomasphic wilh Ge(5)

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Q: 1. Find gcd(a, b), and express it as a linear combination of a and b ((a, b) = sa + tb). (1). а 3D…

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Q: Solve the given SLE using LU-Factorization X, +x, +x3 = 3 x, - x, + 4x, = 4 2x, +3x, - 5x, = 0 %3D…

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Q: If A is diagonalizable, then A is similar to D. Select one: O True O False

A: Given   if matrix a is diagonalizable then A is SIMILAR  to D

Q: 4. Let A %3D {a, b, c}, В %3D {x, у}, and C %3D {0, 1}. Find a) АхВх С b) СхВхА с) СхАх В d) ВxВxВ.

A: Given that: 4. A={a, b, c}, B={x, y}, C={0, 1}   NOTE: As per our answering guidelines, we can only…

Q: Let A = {-i, .,-2, –1,0,1, 2, . i}. Compute the following a) U는1Ai A? = {?} A? = {?}

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Q: Let u = , V = , and w = . Find u + v - 3w

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Q: if| A - B | = | A + B | . prove that A is orthogonal on B

A: Given, A-B=A+B

Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: Prove that if A is similar to B and B is similar to C, then A is similar to C.

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Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

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Q: If Ea, is divergent and 2b, is divergent, then E(a, + ba) is divergent.

A: Taking an example and than we are trying to understand tha statement.

Q: Prove (A = B) = (A v C) = (B V C)

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Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (−1, 2), v = (2, −2)

A: u→=-1,2v→=2,-2a u→.v→=?     u→.v→=-12+2-2           =-2+-4          =-6u→.v→=-6

Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

A: We have to check

Q: Suppose a, = lan 1- 6an 2 + lan 3 and a4 = 47, as = 3, and a6 = -273. Find a1, a2, and az. %3D %3D =…

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Q: show that if Z ~ N(0, 1) and Y ~x²(n) with Z and Y to be independent, then T: n

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Q: Express w as a linear combination of u and v: ? = (4,1), ? = (−2, −1), ? = (2, −2)

A: Let w = (4,1) u = (-2,-1) v=(2,-2) we can write this as: u-21 + v2-2 = 41   -2u + 2v = 4 u - 2v = 1…

Q: Let A = and U = Then A2017U is equal to ... B

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Q: Consider a LU factorization of 3 A = 6 as A=LU. Then L2,1 and U1,1 are respectively equal to

A: solution:-

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: 2. If A and B are mutually exclusive, P(A) = 0.3 , and P(B) =0.47, find %3D (а) Р(А); (b) Р(В'); (с)…

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Q: Compute the following linear combinations for u = (1, 2), v = (4, –1), and w = (-1, 3). (a) u + w

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

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Q: Let a = (– 1, 5, 0) and b = (3,0, – 1). Find the component of b onto a.

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Q: Let z, w E C. Show that |z + w[? + |z – w|? = 2(\z|² + |w|?).

A: Any complex number, Z can be represented as Z=x+iy, where x=Re(Z) , y=Im(Z) . The expression, Z can…

Q: T is self adjoint if (Tx, y>= (x, Ty> o > |(Kr.x>|| o

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Q: Let n=23 and consider the following information, Model One: Y = Bo + B1X1 + B2X2 + B3X3 + B,X4 +e…

A: Solution: Given information: n= 23 observation: k= 3 independent variable  R2=0.8685

Q: Compute d(ū, ū), d(ū, w) and d(ū, w) where ū, ū and w are

A: Given: u¯=12-48, v¯=8-241 and w¯=2-418 To find: du¯, v¯, du¯, w¯ and dv¯, w¯ where d is distance…

Q: Given Jao ao = = 9, a₁ = 36 a1 an+2 = 7an+1 Show that Vn N, n ≥ 1 10an, 20 an=3.2 +6.5n

A: