When A has full rank, the pseudo-inver en m≥n, and as A+ = AT (AAT)-¹ when n A = I, so A+ is a left inverse of A; in the

Q: If x is any positive integer , then the sum of 6x and 11x is always divisible by what?

A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

Q: 16 M = 7 -5 Find formulas for the entries of M", where n is a positive integer. M" =

A: We have to find the entries of matrix Mn.

Q: 23. For any real number a, a ‡ 0, show that a +1 a +4 a +7 a +5 a+6 a +9 a -2 a +3 and a +8 | = 0, a…

A:

Q: Evaluate f1 dy Vy-1 O a. 2ỹ+ 2ln(ỹ – 1) +C O b. 2j – 2ln(/ – 1) + C O c. None\ of\ the\ following O…

A:

Q: Let a,b be integers, not both 0. Show { na + mb : n,m ​​​​​are integers} = iff a and b are…

A: We have to prove the given statement.

Q: Let c, ax, be nonzero real numbers such that e. Find a given that ac² n=3 16 Ch Türkçe: c, a, 3…

A:

Q: 2 and an+1 Зап + 2. Find an explicit Suppose that a1, a2, a3, . .. is defined by a1 formula for a,…

A: Suppose that a1,a2,a3,...,...is defined by a1=2 and an+1=3an+2.find the explicit formula for an in…

Q: Find the argument of 1+i ал with integer a,b b write your answer as a/b for Arg (1+i) =-

A: We have to find the argument of 1+i in the form of arg(1+i)=aπb with integer a, b.

Q: Let S be the set of all real numbers except -1. Define * on S by a*b = a + b + a b. The solution of…

A:

Q: 4+ 3i 3 — 5і (b) 2+ 3i 2 – 3i

A:

Q: Find the smallest positive integer x such that 11x + 567y = 5 for some integer y. Enter x below.

A:

Q: Show that there is exactly one positive number u such that In(u² + 1) + Tu = 2021.

A:

Q: Construct A so thatN(A) = all multiples of(4,3,2,l). Its rank is __ .

A: We have to construct a matrix A so that NA=all multiples of 4, 3, 2, 1 and also find its rank.

Q: Let a, b, c be positive integers such that a is a multiple of c and a2 + b2 is not a multiple of c.…

A: a, b, c are positive integers such that a is a multiple of c.  => there exists some integer x…

Q: 2. Find n and a if: Inx² + In2= In ax"+1

A: Given equation is lnx2+ln2=lnaxn+1. We have to find the value of n and a. Used formula: lnmn=nlnm…

Q: Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 72 percent order a soft…

A: Given information- Percentage of the customers order a square pizza = 0.50 Percentage of customers…

Q: If A = 0 and Ak = 0, for some posit ive integer k , then A must be singular Select one: O True O…

A: The solution is :

Q: Let f:C-R be a function where Cis a closed and bounded interval. Prove that if f is continuous then…

A: The given problem is to prove that the function is maps from closed and bounded interval to Real…

Q: Prove that 13n13 +11n is always divisible by 24.

A: We prove this by induction on n.

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

Q: Estimate the error in using the partial sum of 35 terms of the series > k=1 Error < Hint: Use the…

A: The given series is ∑k=1∞ 6k6. We have to find error.

Q: Evaluate the Boolean power A3 where [1 01 A = 1 1 1 1

A: Boolean Product : Let us consider two matrices A=[aij]m x n  and  B=bijn x p be zero-one matricies.…

Q: Use (9.11) and (9.12) to simplify (ABTC)T, (С-1мс) -1, (АН) -"(АНА-1)"(НА-1) -1.

A: For (ABTC)T by using (9.11) we get (ABTC)T = CT(BT)TAT As (BT)T = B Hence (ABTC)T = CTBAT

Q: Discuss the continuity of the following function: (2* (1– x), x 0 x = 0

A: Consider the given:

Q: For each nonnegative integer n, let Un = (n, -n]. Find U3

A:

Q: Show that a6-1 is divisible by 168 whenever (a, 42)=1.

A:

Q: Let a1, a2, a3, . .., an be real numbers. Prove that at least one of them is greater than the…

A: We prove it by contradiction.

Q: «А B 1)

A:

Q: с. In(х + 2) +Inx —D In(x + 12)

A:

Q: Let r E Rt. Prove that if z – 2x2 +2 2021. -

A: Let x2=t, Now if x∈R+⇒t∈R+ ⇒t2-2t+2≤0⇒t-12+1≤0⇒t-12≤-1which is not possible for any value of t, for…

Q: If gcd( m, 91) = gcd( n,91) = 1 then show that 91|m³7 – n37 %3D

A:

Q: Suppose that there exist integers à and y such that ax + by = 12. What can you deduce about (a, b)?

A:

Q: 2- find aw dw if w = xy + ду +3/1

A: Given is the function w=xy+eyy2+1. We need to find ∂w∂y. In order to find the partial derivative…