Part Iū Proue that if 4aj + 5 b; a;za and bj then Hat 5b

Q: ove that if AB = 1, then B = A- 2, 1 -1 21 and (b) 3 1 1 1 -2 1 2.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: If gcd(m, 28) = 4 and gcd(3,7) = 1 then m = %3D %3D

A: Given: gcdm,28=4  First, we will calculate G.C.D of all options with 28. a gcd4,28=4 ∵ Greatest…

Q: [1 2] If A = then show that |2A|=4|A| %3D 4 2

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Q: a – b -| < 1, if|a| < 1, and |b| < 1. 1- āb - Show that|-

A: From the given information. For , then show that .

Q: Show that if ac|bc, then a|b.Show that if a|b and b|a then a=±b.

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Q: 3. Prove that (An B)² C A × B.

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Q: -3 Let A = and v = -12 -4 -6 -3 Av = %3D -12 -4 -6, Ex: 5

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Q: Show that if a\b and gcd(b, c) = 1 Then gcd(a,c) = 1 %3D

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Q: 5 + 6 x 2- 22 25. 7 3 3 - X 3 3 x 6

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Q: 1. If f(3) - A (3) = 15 and gʻ(3) =- ) (fg)'(3) USTO TO. %3D COMPILE OMPILEDA PILEDAN ED A ) = -3,…

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Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2, express a, in terms of n.

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Q: Assuming that gcd(a , b) = 1, prove the following: (b) gcd(2a +b, a +2b) = 1 or 3.

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Q: I, \B|, A + B, and |A + B|. Then verify -1 1 8. 1 0 1 A = 0 1 1 B = -1 1 8 1 1 -1 0 1 8

A: Given: A=-11801111-1, B=101-118018

Q: Show that gcd(a, bc) = 1 if and only if gcd(a, b) = 1 and gcd(a, c) = 1.

A: Consider, gcd(a, b) =1 and gcd(a, c) = 1. If gcd(a, b) =1 then there exist integers m and n such…

Q: How many elements are in Z5[i]/&lt;1 + i&gt;?

A: Given Data The expression is Z5[i]/&lt;1+i&gt;.   Consider the Z5[i]/&lt;1+i&gt; in the form of…

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: if 1 A = 4 -3 0 7 4 5 %3D 5 0 7 then A is symmetric

A: Transpose of a matrix: Let a square matrix A=[aij]n×n . Then the transpose of A is denoted by AT and…

Q: If 3 -letter words" are formed using the letters A, B, C, D, E, F, G, how many such %3D words are…

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Q: but not こ *6A-エ none of thesce

A: Let us assume two matrices A and B. To prove or disprove if AB=I then BA=I. Let us consider matrices…

Q: I elements is A, then the

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Q: Exercise 16: Write up three proofs for the above six theorems. (You should be able to do all of…

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Q: snip

A: Solution: Consider the given matrix: A = 1-324-1-2-513 We have to find A1 A1 =max1≤j≤n ∑i=1naij  =…

Q: 2. and as= Determine ifb=-1 =-2 is a linear combination ofaL az

A: Follow the procedure given below.

Q: (a) Show that if (a,342) = 171 and (b, 342) = 171 then (a+b,342) = 342. %3D %3D (b) Show that if (a,…

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Q: S 10х T U бх + 3

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Q: (b) If = 1, show that i=1

A: We will use Arithmetic Mean (AM)and Geometric mean(GM) inequality  to prove the given results…

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a,= 2an-1+ an-2, express a, in terms of n.

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Q: Find a and b such that 2 1 = a -4 + b -4

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Q: The_____ of A and B consists of all elements in either A or B or both.

A: The_____ of A and B consists of all elements in either A or B or both.   The answer of the above…

Q: 3. Show that 1 > 0. 4. Show that if a > b and c < 0, then ac < bc.

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Q: Show that lcm (a,b)=ab if and only if gcd ( a,b)=1.   Thank you! <3

A: Solution

Q: Q.31 If a+b+c=5 and ab+bc+ ca=10, then prove that a +b³ +c³ – 3abc=-25 Q.32 Prove that :

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Q: Show that if a \ b and gcd(b, c) =1 Then gcd(a,c) = 1

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Q: If a =(2,3,-1) ,(1,6,0) ,(2,1,3) prove that Aa^-1 =A^-1A=I Please show all the step

A: Given matrix is, A=23-1160213

Q: If a = qb +r. then gcd(a, b) = gcd(a,r).

A: In this question, we have to check the gdc(a,b)=gdc(a,r) if a=qb+r

Q: If a 3 are ordinals and a C 3, then a € 3.

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Q: 21 41 Verify the following directly if A = 1. B = |; .c = [, а. A(ВC) %3D (АB)C b. А(B+C) %3 AB + AC…

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Q: [1 2] If A = then show that |24|=4||| %3D 4 2

A: Introduction :We have given a 2*2 matrix A. We have asked to show that |2A| = 4|A|.

Q: Find, if possible, AB and BA. (If not possible, enter IMPOSSIBLE in any single 3. 1. -4 2 A%3D 2 -1…

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Q: Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than…

A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove &lt;-…

Q: Let A = 1 2 1 and v = If the entries of A and v belong to Z3, what is the third entry of Av? Answer:

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Q: het A=" and let fce)= 20x²-4X+5. Find 3 4 -3 り 3 4 ) fCA)

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Q: linear algebra, 2.5 question 5

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Q: Section 1.2 40,6,8 4d, Prove the follo caing for nz li and only if

A: Suppose nr&lt;nr+1 Then, n!n-r!r!&lt;n!n-r-1!r+1!1n-r&lt;1r+1r+1&lt;n-r2r&lt;n-1r&lt;n-12 Hence if…

Q: 0. Prove that (i) |4' ||, =||4||,, and (ii) ||4' A|| -||4|-

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Q: Final marks in Maria's Data Management class are based on 70% for term work, 15% for the exam, and…

A: From the given information we find term marks

Q: prove that if a>4 then (a-2)^2>4

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Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…

Q: Find the generalized union and intersection: 1. A = {1,2,3,...} 2+1 Q-(무)

A: Let us find the generalized union and intersection of the given indexed set in the next step.

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.