1. Compute n, μ, EX, and EX² 5, 7, 3, 4, 1 2. Compute n, EX, (EX)², and EX² X 7 5 6 2 3 f 2 3 4 2 1 1 5 3 4

Q: if a= [1 4 2; 5 7 3; 9 1 6], then C=det(a) = C = 89 C = -89 O C = 89.000 = None of the above if…

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Q: 1. Let A = {a, h, g}, and B = {3,6}. Answer each of the following questions. %3D (а) Ах В (b) В х В

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Q: let u=(1,2,3), v=(3,2,1) and w=(4,5,6) u.(2v)= Select one: 1/20 20 -20 -1/20

A: The given vectors are: u=(1, 2, 3)v=(3, 2, 1)w=(4, 5, 6)

Q: Questions 1 and 2 refer to the following definition. The operation * is defined for all integers (x,…

A: Given data :-     The operation * is defined for all integers (x,y) as x*y = x2+3y We requied to…

Q: 2. K-5InX+3 find dw dr dw

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Q: Match each direction field with its differential equation.

A: Given the differential equation is                                            dydt=-1.

Q: A car traveling along a street needs to pass through 4 intersections with traffic lights. If each…

A: Introduction: It is required to find the probability mass function of pmf of X.

Q: x24x 3 + x 1 = xp 7x2 - 2x + C In)x - 1C Inx C 6x 3 Inlx 1 + C 2 5x + 2 Inx 1 C

A: Consider the integral is

Q: 4- Suppose that A = {x1 = (2,0,1), x2 = (1,–1,4), x3 = (-1,–2,1)} and B = {y, = (-1,0,2), y2 %3D %3D…

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Q: 1 = 4, x, = (1, 0, 0) 12 = 2, x, = (1, 2, 0) 23 = 3, x3 = (-7, 1, 1) 4 -1 8 A = 2 1 0 3 4 -1 8 1 Ax…

A: Eigen values and vectors

Q: 1 Compute the quantity, w, using w= - 1 w•w - 7

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Q: 6. Evaluate the det A where A = 1 0 -1 2 4 24 3 1 0 1 0 041 44

A: Given Matrix: A=14230144-10102041 To find: The determinant of the matrix. Concept used: i) There are…

Q: ZZ= X+y O x² +y² x² - y O

A: The given expression is zz. Let z=x+iy. Then, z=x-iy.

Q: Let R = {(3,4),(1,3),(4,2),(4,1)}, Then R² is given by O (1,3),(2,1),(3,2),(4,3)} O {(1,3).(2,1).(3,…

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Q: 6. Compute 1,= de for p= 0,1 10

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Q: If X is the number of heads obtained in four tosses of a coin, the 1 is 1+X mode of Y =

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Q: 4. Let, a, = 1, az = 2, b, = 0, b2 = 1, for n 2 3, an = 2an-1+ bn-1 for n 22 bn = bn-1+ an-1 express…

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Q: 1. Find 4 -53 0 | | Td 205 -3 4 1.

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Q: Expand la In 3 Inx Iny? Inz 2n 3+ 2mx+ 2lmy hz a. 2h3+ 2hx+ 2ny- 2hz In 3+ Inx+ 2hy- nz

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Q: 18

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Q: Scatterplot 1 Scatterplot 2 Scatterplot 8- 8- 6- 6- 6- > 4- > 4- 4- 2- 2- 2- 0- 0.2 0.4 0.6 0.8 i 0-…

A: The correlation coefficient is lies between -1 to +1

Q: 9. Determine the value(s) of k such that (2k, 3, k + 1) x (k-1, k, 1) = (1, -2,2).

A: (2k, 3,k+1)*(k-1, k, 1)=(1,-2,2)Find the value of k.

Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

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Q: If then A-¹- = A = [1 0 0 07 3 1 0 0 24 1 0 8 55 1

A: The given matrix, A=1000310024108551 We have to find an inverse matrix of A.

Q: 4. Find z, and z, such that, 2iz, +iz, 2+5i and = 9-11i 3i z,-2i 2, 4 =i+1, z, = 3+4i (b) z, = 3-4i,…

A: Solution:- let z1 and z2 be the different ccmplex number i2= -1 i3=-i

Q: 3. Consider A={m,a,t,h}; C={x:x=3n,1sns4,neN}; B={s,t,e,m} ; D={x:x=2n,15n S6,nEN} What is ANB?

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Q: What is m 24?

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Q: Let A=(1,2,3,4), B=(00,01,10,11), C3(x,y,z). f1 = (1,00),(2,01),(3,01),(3,10) (4,11)} f2 = {(1,x),…

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Q: Let 1 -2 1 -1 -3 1 3 A = -2 -1 1 -1 3 0 1 3 0 -4 Then nullity(A) = 2 4 3 O None

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Q: Example 1 ܝ 13 [²²dx=2 [²x²dx=2+ = = 18 2. 3 10 a3

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Q: 8. If W = and V =, compute W x V.

A: To compute w*V from the given vectors.

Q: -10 3. Let v = (-1,3). Draw v, -2v, and 3v in standard position. 101 4 2 10-8-6 -4 -2 2. 4. 6. 8 10…

A: Given v= < -1, 3 > To represent  v find the point (-1,3) on the coordinate plane, the connect…

Q: 5-24 If x is N(0, 4) and y = 3x², find ŋ,,o,, and ƒ, (y).

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Q: 6. S(1+ 3*)²dx

A: First of all we need to integrate the function then apply the limits

Q: 7. Let U = {-5,-4, -3,-2,-1,0, 1, 2, 3}, A = {-1,0, 1} and B = {-4, -2,0, 2}. %3D Prove that (A U…

A: Explanation of the answer is as follows