(c) A(BC) = (AB)C [Associative law for matrix multiplication]

Q: et a =i- 2j + k and b= 2i+j +k. Show that la + b| s lal + b|

A:

Q: Q3 Prove that In Coth x 1

A:

Q: Let A = {1,{2,3}}. Find P(A), n(A) and n (P(A)).

A: The power set of a set is the set of its subsets. The expression nA represents the number of…

Q: How many zeros does the function below have 1 31 - g(1) + Vi +1- 3.1, (-1,1) O A) 4 O B) 3 C) 0 O D)…

A: Given:

Q: 7. Evaluate using the residue theorem eir dx x2 +1

A:

Q: Ty int Let z = Then. 5z2-5y2 az

A: topic-  implicit differentiation

Q: Let a €R be algebraic over Q. Prove that Q(a) # R.

A:

Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

Q: Show that if x > 0 and |x² – 9| < 2, then |x - 3| < 1.

A:

Q: (c) Prove that r| +11 36 T-1 2 +36 for all real I.

A: We have to prove that the following inequality holds: x-11x2+36≤x+1136 for all real x. We will use…

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

A:

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

A:

Q: re 1 da Ji rVI- (In x)²

A:

Q: A = 13 47 AXB = T² 1 1347 e 2 23 AXB ] = 1² mi find b

A:

Q: Which of these functions from R to R are bijections? (Check all that apply) Check All That Apply A…

A:

Q: (B) Prove that (Q,|·|) is not complete.

A: A metric space (X,d) is said to be complete iff every Cauchy sequence in X converges to a point in…

Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

A:

Q: Find the term of (a – 2b)3 that has b in it. |

A:

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: Find all values of z such that z5 =1 - i.

A: Given: z5=1-i, To find: All values of z.

Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: a) Use Newton interpolation to find the unique cubic polynomial f that passes through the points (0,…

A:

Q: B = {1/2 + 1/6n | n ≤ N}.

A:

Q: 6. Show that Autoq(Q[3], 5]) is finite.

A: To show: Autℚℚ35,53 is finite.

Q: State whether the following statements are True or False. If they are true, provide mathematical…

A: Two vectors are parallel if they have the same direction or are in exactly opposite directions .…

Q: Show the roots of x² - (a – 1)x – 2(a – 1)² = 0 are real. -

A: To show that the roots of  are real.

Q: 1+1 3t2 1+* t--1

A: Here I am attaching image so that you understand each and every step.

Q: (A) Find ( 3- 5 i )6 using DeMoivre's Theorem.

A: De-Moivre's Theorem states that if  a complex number z in polar form is given by…