Suppose that T is a linear transformation from a vector space V to a vector space W. Furthermore, suppose that {61, 62, 63, 64} is a basis of V and {T(b¹),T(b²), T(b³),T(61)} is a basis of W. • What is the dimension of W? What is the dimension of the image of T"? ⚫ Why is T an isomorphism?

Q: 6. Theorem 131

A: The figure of the circle is given by Theorem : ∠Q = 12mPSR⏜ - mPR⏜ To evaluate : The value of ∠Q

Q: C_A* UI

A:

Q: let à = (3,4,5) and To (5,2, 6) a Find (2-6) x (a+b)

A: We need to find out the cross product.

Q: Show that im n /-

A: Limit of the sequence

Q: 2. Show that cÃ=cA.

A:

Q: If gcd(a, b) = lcm(a, b). then a = b. %3!

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Q: Find Chai

A: For n=1, 0, 1+1n=0, 1+11=0, 2For n=2, 0, 1+1n=0, 1+12=0, 1.5For n=3, 0, 1+1n=0, 1+13=0, 1.333For…

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A:

Q: Solveit. 2 3X

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Q: B- Gurtient Rule

A: Given :           f(x) = 2x2 + 5x - 1x   To Differentiate f(x) using Quotient rule.

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

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Q: 8. [ tan’rd.r

A: We have to find the integration of given questions.

Q: 1)r =4rsin e

A:

Q: Find each set U={2,3,5,7,11,13,17,19} B={2} Find B'

A: Given:       Set U=2,3,5,7,11,13,17,19             B=2     B'=set of elements of U that are not in…

Q: Suppose that A= {a,b,c,d} Then |A| =.?

A: Let X be a set , then X be number of elements in set X

Q: Haw it Veszy, 22,4x+77 ?,X? y?, ye> find (curt w)-v at (4,0,2) W=<3Z

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Q: 6. to 16 2.

A: Our Aim is to solvex216+9x2=2x4-32+12-(i)

Q: Find U4,, Ñ4, , if A, = {0,1, 2, .}, A2 = {2,3, ...}, ., An = {n,n+ 1,. %3D

A: For 1st part we have A1 U A2 U......An ={0,1,2,3,.........}

Q: tan' rdr

A:

Q: b22 Such that/2/-1E andArg 4.

A: We find complex number

Q: 2. 25

A: Given: ∫-7-52dyy4y2-25

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A:

Q: Suppose that A = {red,white} and B= {white,blue} Then AUB=.?

A: We know that A∪B = x : x∈A or x∈B

Q: Find, (x²e*dx

A: use integration by parts take the rule is

Q: ( − 1,1) n [04]

A: To find intersection between given two intervals.

Q: Find the general suhetion of to

A: Given a differential equation, y"+2y'+17y=0 To find the general solution.