7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

Q: Show that: If |z| = 1, then: z' + 4z + 5 z2 + 5z + 6

A: Given: z=1 Then show that: z3+4z+5z2+5z+6≤5

Q: Prove that: m3 = m – 3m,m, + 2m²

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: 11. If QM = 6x - 11 and MR = 2x + 9, find MN. %3D

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: (c) 2, 3, 4+ V10 and 4. V10 are irreducible elements of R.

A:

Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

A:

Q: Let X - N(2, 4). Calculate P[X2 – 4X < 4].

A: P(X2-4X≤4)=0.7602

Q: In Z[V3], the element 2+v3 is:

A: Unit Given element is a unit

Q: 3. 'N M2CAN = 18x - 1 MZMAT = 15x + 20 Find the following: M2CAN = MZMAC = MZTAN = MZMAT = MZMAN =

A: Adjacent opposite angle are always equal so equate both and get the x value. Then put the x values…

Q: 4. Conclude that n2 n=1 ||

A:

Q: (2) Show that for any integers a,b we always have a? – 4b # 2. -

A:

Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: 2. If BDbisects <ABCand m<ABD=10x-3 and m<DBC=2x+5, find m<ABC. A

A:

Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

A:

Q: Let, a, = 3, a2 = 4 and for n2 3, a,= 2an-1+ an-2 + n + 1, express a, in terms of n. %3D %3D %3D

A: The nth term of A.P is given by an=a+n-1d we have,  a=3,d=4-3=1an=3+n-11=2+n we get,…

Q: 2. Suppose A is an m x n matrir, x ɛ Rª and Ax = b. Then b is in 1) R" | 2) R™ 3) RmfnT 4) R™n

A: Given :  A is an mxn matrix , x∈Rn and Ax=b   To find :  b is in which space of the given spaces.

Q: " Show that the integers m = 3* . 568 and n = 3k. 638, where k > 0, satisfy simultaneously t(m) =…

A:

Q: b) Prove that 20 15 k Σ 3.2-Σ 96.2 %D i=5 k=0

A:

Q: Is the equation Ax = b consistent for all b in R^3? Explain.

A:

Q: Show that for all n, m∈Z if n+m is even, then either n and m are both even or n and m are both odd.

A: Use the results of addition of integers.

Q: Prove that in Q(/-5) we have (3,1+ 2v-5)(3, 1 – 2-5) = (3).

A: To show the equality, first we take an element of the product and show that it is in (3) and then we…

Q: 3 10. Show that R² span

A:

Q: 2. Compute the value of | V25–x² dr

A: Given data:   The given integral expression is I=∫0525-x2dx.     Assume x=5sint, and differentiate…

Q: Let, a, = 3, a2= 4 and for n2 3, a,= 2an-1+ an-2, express a, in terms of n. %3D

A: we have the nth term of A.P is given by  an=a+n-1d here,  a=3, d=4-3=1an=3+n-11=2+n we get,…

Q: What element corresponds to (2,3) of (A^T) x (B^T)? What element corresponds to (3,1) of (AxB)^T?…

A:

Q: 22. If 6log2x =18 , then x is

A:

Q: 5.1. Show that y2 , V2 , and v3 + V2 algebraic. are

A: We will use definition of algebraic numbers

Q: 3. Let r and y be positive integers. 4. Let a, b, c e Z. If c divides a +b,

A:

Q: (27) Let X = P(2) and )E(5-5x) finc

A: Given X≈Pλ That is, EX=λ

Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

Q: 10. Prove that Âx x= A.¿)B. CĀ. B) where. A.ai.+azj.+a3k Babi.itb2j.t.b3.k. !! .. ..

A:

Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

Q: 3. Which statement about k (z)= 3z -7z+2 is true?

A:

Q: 2. Show that if a is an integer other than 0, then a) 1 divides a h) a divides 0

A:

Q: Supppose that X ~ N (2; 3). Find P (1 &lt; X &lt; 4).

A:

Q: (1) Disprove the statement "For all integers a, b if a | b2 and a < b then a | b." by giving a…

A:

Q: 10. Given à = 5î – 2ĵ – 2k and B = 4î + ĵ – k, compute Proj A. %3D

A:

Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

A:

Q: If (ar + bx) = 4n and n+1 k-1 (ak - bx) = , then > ak = n+2 k-1 k-1

A:

Q: Show that  1/3 Tn + 2/3Mn ) = S2n.

A: By definition, Tn=12∆xfx0+2fx1+....+2fxn-1+fxnMn=∆xfx1+fx2+.....+fxn-1+fxn…

Q: 9. If VW = 9x - 11 and SU = 16x – 12, find WT.

A: Given VW = 9x - 11 , SU = 16x -12 , WT = ? STUV is a rectangle , W is the midpoint of diagnols SU =…

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: Show that if (B) (C) = 3x N (AB)_ (BC) (CA) =y, N (A) = x, = 2x, and N N N then the value of neither…

A:

Q: and (A) (B) = x, = 2x, = 3x, Show that if 8. N N (AB) _ (BC) _ (AC) 1 = y, then the value of neither…

A:

Q: Prove they are equal 4 = 7(2x+ 1) - 5x -3(3x + 1)

A:

Q: Show that the integers m = 3k . 568 and n = 3k . 638, with k E Z>o, satisfy simultaneously $(m) =…

A:

Q: 2 4-x2 x2 +4 1 2x

A:

Q: Show that yn Z, if n³+5 is odd then n is even

A:

Q: b If K = 4.1 x 10-6 then pK, Submit

A: This is a basic log problem