Find JA|, IB|, A + B, and |A + BỊ. Then verify that |A| + |B| # |A + B|. 15 0 1 -1 A = 1 -1 0 B = 5 1 1. 1 1 0 1 1. (a) |A| (b) |B| (c) A + B (d) |A + B|

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

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Q: 1 リ=ス,メ=0; Xe2, y=or abt. A the x- Axls

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Q: n -r Prove that („",) : r+1

A: Combinations: Combination is the selection of n items taken r at a time is

Q: z -7 2. prove that: Im(z)= 2i

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Q: (2) |R| = |2N].

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Q: 14.Let A= 3+2i 0 2 1+i 1-i B-( + ?) and B= Find AB.

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Q: Q5: prove 1) e2-j3n-e² = 2) |e²| = ex

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Q: Prove that (x - i) = > xi i=1

A: We will prove the following result.

Q: .Prove that A =B² = C² =I. 0 -1 Given A = B = and C = 1 0 i

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Q: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

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Q: 5. If Z1 = V3 - 2i, Z2 = -i+1 and Z - 3= 4i – 2. Evaluate (i) Re{3Z -5Z +2Z}} (ii) |(1+ Z, + Z3)(i –…

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Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: : 2 < x < 4} and B = {x € R : –4 < x < 1}. Prove

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Q: O show that 2. I| a+ V 1= 11 + 1i if and only if ū. ů =0 %3D

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Q: Prove that Ek=0 C) 7n-k . 2k = 32n %3D

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Q: a) Show that E-o(-1)*(")=0, and then verify that () + C) + C') + -- - C) + (") + (") + -- .. b)…

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Q: 3. Show that (1+i) = 2i

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Q: Prove that Σ = 2" . a. x=0 b. = 0. x=0

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Q: ez = -2

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Q: [D²,2²] = 2(2&D + î) 2(2£D + î) Prove that

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Q1) If B = B-1 then B = I or B = -I. Prove or give counter example. %3D

A: A detailed solution is given below.

Q: TRUE/FALSE If A = A−1, then A must be equal to either I or −I.

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Q: 3. Compute |(1+ i)(1 – i)(1 + 3i)| .

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Q: %3D n-0o 2n

A: Given. We are given a limit and we need to prove that the limit of the given function at infinity…

Q: If Z1 = 4 + 5i and Z 2 = -1 + I,  express in the form a + bi  (i) Z1 + Z2   (ii) Z1 – Z2

A: Formula used  sum of two complex number is given by  (a1+b1i)+(a2+b2i)=(a1+a2)+i(b1+b2)

Q: -10 -4 3 6 Qs: A- Given A = L -4 and B = -8. 2 -14 -28 Prove that: - AB+BA = -7 14

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Q: 4. Let z = -4 + 3i and zw = -7 - 2i. By showing clear steps, find w in the form of | | a+bi.

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Q: 2 Xi. にく prove thate 2.

A: Given that  We have to prove the given expression:

Q: iii) a) Prove that Pa(-x) (-1)".Pn(x) u (2n)! 22 (n!) b) Prove that P2n(0) = (-1)".- %3D

A: To prove- Pn(-x)=(-1)n.Pn(x)P2n(o)=(-1)n.(2n)!22n(n!)2

Q: Prove that Co +2C, +4C₂ +8C3 +..... +2 °C₁ = 3^

A: Given problem:- Prove that C0 +2C1+4C2+8C3+...... + 2n nCn =3n

Q: 8. What is v–121+ 15 in the form a + bi? 0 + 4i 0 – 26i 15 – 11i O 15 + 11i

A: In complex number, a+ib, a is a real part and b is a imaginary part. We can write,…

Q: H PROVE : กะ1 [-¹-², ¹+ ²] = [1,1] 1 t

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: 3. The solutions to P(x)=0, in simplest exact form, are z = -2, -d±eVf. The values of d, e, and f,…

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Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

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Q: express z1z2 and z1/z2 in the form a+ib. Q. z1 =4−i, z2 =1+3i

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Q: a- If A = -1 %3D 2 and B = -41 prove that (A + B)T = AT + B". 12 [1/2 - If A-1 =1/2 -1/2) and |A| =…

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Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: JJ. JUA X ABD) 224 ABE) 16 36. g(x)=2x -3x² +5x+3 ACD) 1 АCE) 2 37. h(x)=x -4x³ +3x² +8 ADE) -3 BCD)…

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Q: Q4: 1- Prove that (1– i)? + (1+ i)² = 0 . %3D 2- Put in the form a + ib ((1+ i)²)² - ((1- i)²)².

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Q: 2. 2. (xij-X-) Xij-.. prove thate

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Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

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Q: Then prove that 3 (i) P (AUB) > 1 (ii) <P (An B) S 10

A: Answer: From the given data, P(A) = 3/5 and P(B) = 1/2

Q: 3) Calculate: AВ-ВА , АС-СА , ВС-СВ Where 1 1 0 1 A 1 1 B -1 1 0 0 V2 Vzi 1 0. 0 -1 0. -1

A: I have found each product term one by one

Q: 3. Prove that (An B)² C A x B.

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Q: Show ther' 3 2

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