-5 14 -3 -2 -1 5 4 3 2 -1 -2 -3 -4 -5 h(x) The function h graphed above is: Increasing on the interval(s) Decreasing on the interval(s) 1 2 3 4

Q: Why must nCr always be less than or equal to nPr for any given n and r

A: Permutations and combinations are given.

Q: 50 50 51 7. + 40 39 40 • () - €) (") - () () - () () 7 8. 4 10 9. 2 10 8 8. 8 8. 10. + 2 3 6.

A: We can solve the given problem using concept of fractions.

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: れ+5

A:

Q: Find the maximum value of a, x, +a,x, + .+ax to the condition that x +x, +. + x =1 for given…

A: We need to find the maximum value of a1x1+a2x2+a3x3+...+anxn to the condition that…

Q: Example 7.4.1. If a = (2, -1, 3) and b (1,2, 1), find a x b.

A:

Q: finD 1) 2) g(s (x) a) p(x) x?-2x+2 b.) g4)==3x t. %3D cl.) s(x) = x-1 4) Cx))

A: Given that px=x2−2x+2, qx=3x+1, rx=x and sx=x−1. 1 We have to find the prx. prx=pxUse…

Q: NCx) = x² - 2x - 5 MQx) = 2x+3 N of M

A:

Q: Use membership tables to prove that A – (Bn C) = (A – B) U (A – C). %3D |

A: We want to prove the set identity A-(B∩C)=(A-B)∪(A-C) using membership table . Here we will use…

Q: 2 solve the following set of three equations by Gramer and by A XI-X22X3 = 1 2X1 - X3 = 2 X₁ + X₂ +…

A: Given the system of equations: x1-x2-2x3=12x1-x3=2x1+x2+x3=3 Solve using Cramer's rule.

Q: 3) (- .) How many ordered quadruplets (a1, a2, a3, a4) of non-negative integers, where at least one…

A: We have to find the how many ordered quadruplets (a1, a2, a3, a4) of non-negative integers, where at…

Q: 17 3. Evaluate: de (r- 1)(2 + 16)

A:

Q: III. Determine whether the statement is true or false. (Example: if B+2 10, then 4 37 is FALSE…

A: Given that:                            1. -15<152. 8+3=11 Or, 5 is an even number3. 1=2 and 15 is…

Q: H.W 1.: Use Cayley-Hamilton to find 4 -1 A' and A Where A = [2 1 1 0 1 0 11 2 ]

A: Find characteristics polynomial and use caylay hamilton theorem

Q: 1. (P16, Page 11,.. ) Use the Method of Proof by Contradiction to prove that 3 ¢ Q. You may use the…

A:

Q: I. True or False. 1. N is closed under subtraction. 2. Z is closed under division. 3. Vx2 = -x if x…

A: A detailed solution is given below.     (As per our guidelines, We are supposed to answer only 3…

Q: Find the rank- 1 approximation of

A:

Q: 5. A. undefined B. 2 × 2 Consider (a) What is the size of QTP-¹? P= A. -1.5 B. -2 = [1 C. 2 × 4 D. 4…

A: Given: The matrix P=4611 and Q=22341-120 a) Find the size of the matrix QTP-1 b) Find the entry 2,1…

Q: 5. Show that 1.2+2·3+3.4+...+ (n − 1)(n) = (n³ − n)

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Q: 11! 1.) 5!x4!x3! 2.) Р(8, 5) 3.) Р(12, 4)

A: Our aim is to solve the following :  1) 11!/(5!*4!*3!) 2) 10!/7! 3) P(8,5) As per our guidelines, we…

Q: 1. (a) 2 Let = (1, 0, -2) and = (-4, 2, 3). Find a real number x such that (ট' –æè) ⊥ à. (b)-1 (c) 3…

A: Let .To find a real number  such that .

Q: 10. Let a = (1,-1,2), b = (2,0,−1), and = (3,-2,0). Evaluate or explain why the expression is…

A: The vectors:

Q: Prove that gcd(a + b, a − b) = ged(2a, a − b) = ged(a + b, 2b).

A:

Q: What conditions, if any, must be set forth in order for a + b to be equal to n(A U B)?

A:

Q: 6. The value of f A. + C B. C. D. (4-x² +C 4√4-x² 4√4-x² dx (4-x²) 1.5 +C +C

A:

Q: Find z-transform for 8 © x(n) = 5ucn) - 2 (055 un) = 5 e(n) - 2 (0-5) u(n)

A:

Q: (1+a-c), (c) ₂F, (_n,‚a+n;c;1)=(-1)" !

A:

Q: Find all positive integers n such that 2" – 1 | 3" – 1. - -

A: Given 2n-1|3n-1 ,  for n∈ℤ+ To find if the statement is true.

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

A:

Q: 2 Let A = 1 (a11 + a22) A 2 Show by explicit calculation that A² and (a11a22-a12a21)I are equal.

A:

Q: . Show that sup{3 – 2 : n = 1,2, ...} = 3. %3D

A:

Q: Compute. 13 2) Σ k

A: Given, ∑k=113k2

Q: -2 1 2 -1 1 -1 2. LetA= Then find A-1 if it exist. 1

A:

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: -1 -2 -3 -4- 1 2 Let A = 1 1-

A:

Q: DIVISION BYt (:) - {}> 81. Show that In %3D

A: