Prove and generalize the following identity P(AUBUC) = P(A) + P(B) + P(C) - · P(AB) = P(AC) · - P(BC) + P(ABC)

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A: Solution: Step-1                         Given if a = 4, 0, 4 ,b = 3, 4, -4, and c = 0, 4, 5, show…

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A: Determine the value of k

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Q: - j6) (60-j80) 2 329) EX(16

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A: Given :         a + ib = 3 - i2 + 3i + 2 - 2i1 - 5i   To find a and b.

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Q: Find the value of q such that (3 + 4i)(1+2i) (1 + 3i) q= = q(1 + i).

A: To find the value of q such that,  3+4i1+2i1+3i=q1+i

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A: Given: ∫06∫012-12y∫013(12-2y-x)xdzdxdy

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A: This question asks to find the adjoint of the operation B^=2|0×1|-i|1×0|.

Q: Let u = (5,5,0) and v= = (5,5,5√√2). Compute |uxv|. Then sketch u, v, and uxv. |uxv= (Simplify your…

A: I have explained everything with in the solution. Please go through that.

Q: -1 Find the minors and cofactor of A given by 2 -1 1

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A: Introduction: The formula for de morgan's law is given by, ~(a∧b)=~a∨~b~(a∨b)=~a∧~b

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Q: CALCULATE THE FOLLOWING USING MINOR COFACTOR AND COFACTOR EXPANSION 3 -8 2 A= 2 -6 3 4 4 2

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: Q1) Find the inverse of A (1 00 A=2 1 0 5 4 1

A: A=100210541

Q: tan(z1) 0.9947 + 0.1462i 0.0364 1.0047i

A: The definition of tangent function for complex number is tanz=e2iz-1i(e2iz+1). Use 4-2i for z1 and…

Q: b) Let {(-2,–6), (–1,5),(0,4),(1,3)} and {(-2,–18), (-1,–7),(0,–4), (1,–3)} be the point-value…

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Q: しEgt やと1 fnd X,yiflzxti}{y2)~-2-91

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Q: Let 4 1 - 3 -2 -9 and 1 A =| - 3 В C =| 0 3 Prove that 5 - 2 -1 1 1 – 4 | (BA)" – A" B" + AC = AC,…

A: (BA)T - ATBT + AC = AC In LHS, We know that, By the properties of Transpose, (BA)T = ATBT .…

Q: ii) Use trigonometric substitution method to evaluate f |4x

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A: Given: limx→3x3-27x2-9

Q: S(sin2z – 3cos2z)°dz

A: Here, (sin 2z-3cos 2z)2 =sin22z-6sin 2zcos 2z+9cos22z=sin22z+cos22z-3(2sin 2zcos 2z)+8cos22z=1-3sin…