1. [10 marks] In MATLAB, define z = [10 40 20 80 30 70 60 90]. (a) What vectors are specified by z(1:2:7), z(7:-2:1), and z([3 1 4 8 1]). Ex- plain your answers. (b) What is z after each of the following commands? Explain your answers. zeros(1,4) zeros (1,4) = zeros(1,5) z(1:2:7) z(7:-2:1) %3D z([3 1 4 8 1])

Q: 1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is…

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Q: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

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Q: 2.Show that the following Vectors form a Wasis tor Pg. 4.ct-11.(t-1",(t-1'

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Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

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Q: 1. Consider the vectors 1//3 n= -1//3 1//3 V=- 2 (n) and develop 2.

A: As per Bartleby guidelines, for more than one questions asked, only first is to be answered. Please…

Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

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Q: 5. Show that the vectors a = 3i- j+4k, b = i- 3j – 2k and c = 4i – 3j+2k are linearly independent.…

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Q: Find a vector v satisfying 3v + (5, 20) = (11, 17).

A: To find a vector v satisfying 3v+(5,20)=(11,17).

Q: Find a nonzero vector c in R^3 such that Ax=c is consistent.   A = 2 1 1 0 -2 -2 2 4 0 -1 3 0

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Q: -91 Let y = -9 and u = -6 *₁ = -4. Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

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Q: 6. Consider the vectors u = (1,–2), v = (4,3), and w = (9,4). Find scalars k and k2 such that w =…

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Q: 5. a) Prove that -2-M u-+ for all vectors in R". b) Explain parts a) geometrically.

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Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b,…

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Q: Refer to the vectors u, to ug. -5 1 1, u2 = u3 = U4 = -5 U5 4 4 Compute projs u8, where s = span{u5,…

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Q: 7 Prove or give a counterexample: If v1, V2, . . . , Vm is a linearly indepen- dent list of vectors…

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Q: 5- Suppose that the vectors x = (1, –1,1), y = (1, –1,2), z = (2,2,0) in R3 then A: x is orthogonal…

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Q: 2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0); ez = (1; 0; 0); Write down the…

A: Solution :-  the given vecots are e1 = ( 1; 0; 0 )  , e2 =  ( 0; 1; 0 )  , e3 = ( 0; 0; 1 )  and  (…

Q: Q4. Prove the following generalization of Theorem4.5. If vị, v2, V3, .., Vn are pairwise orthogonal…

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Q: suppose M is the set of all real column vectors R4 whose components are equal , then the basis for M…

A: suppose M is the set of all real column vectors R4 whose components are equal , then the basis for M…

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Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: to = [0 3 4 2]" v = [1 1 2 1]"

A: Handwriting solution.  { v0, v1, e1, e4} forms a basis for R4.

Q: 5.3 ® Use the inner product = 24, Vi +Uz Vs z in R? and the Gram- Schmidt ortho novma lization to…

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Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

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Q: Suppose M is the set of all real column vectors in R' whose components are equal, then the basis for…

A: See the detailed solution below.

Q: --8 / 15 11 / 15 -2 / 5 2 / 15 4 / 15 2 / 15 1/ 15 8 / 15 4 / 5 -4 / 15 -Let vi = V2 = , and vz =…

A: A set of vectors are said to be orthonormal if each pair in the set is orthonormal. A pair of…

Q: #15. aib are liearly indepandant vectors in IR? Let F= Span faib, 2ar3b}. Then the dmensian of A) I…

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Q: Let v1, v2, vz be the vectors in R defined by 30 -17 7 -3 v2 15 V3 = -14 -12 -14 18

A: Solution is given below:

Q: Let x = (2, 5, 1) and y = (−1, 3, 2) be two vectors in R3. Compute xTy. Compute xyT. Are x and y…

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Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

Q: Which one of the sets of vectors (given in Matlab notation) is linearly independent? OA 2:4:61…

A: by using linearly independence  and dependence

Q: 19 - By using the definition of the dot product, which vector is orthogonal (perpendicular) to å =…

A: Dot product of two vectors

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: 50 Express the vector b = – 11 as a linear combination of the %3D – 48 - - 14 5 - 10 - | - vectors…

A: the question are based on the concept of linear combinations. we will form the system of linear…

Q: Determine a particular vector z3 so that the following set of 3 vectors are independent: a Z2 = 23 =…

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Q: 2 Consider A = -2 null(A). 4 2 2 4 -4 -2 -2 -4 -2 0 1 Give a set of vectors that spans each of im(A)…

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Q: Use the Wronskian to determine if the function vectors 7,= x? + e* and 72= e²x are linearly…

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Q: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

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Q: 12. Let Q C R such that number of vectors in Q is (6) then Q is linearly independent O True False

A: The subset possible with full 6 vectors should be equal to R^6. For Q to be linearly independent its…

Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

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Q: Consider the vectors in M22 then S= {x1, x2, x3} is linearly dep Select one: O True O False

A: The solution is given below

Q: 4.5-5 Show that, for any 2-vectors a and b and any particular vector norm, J||a|| - ||b|| < |a - b||

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Q: (1) We have the following 4 vectors v1, v2, v3 and v4. Prove that the vectors are linearly…

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Q: a) Detemine whether this set of vectors is orthogonal? Q. No. 3 -2 8. 4 1 b) Detemine if the…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 7. Show that 3-{(; ) ( ) ( )} -1 2 S = 2 1 6 9 is linearly dependent in M22. Write one of the…

A: According to our guidelines I solve only 1 question, so kindly request you to repost the remaining…

Q: 1. Compute the angle Pair Of vectors in Standard inner producy on Mzz. between tre following Mzz…

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Q: (S.15). Let u1 =(-1,1,3), u2 = (2,1, –3), uz Find expansion of the vector v = (-3, 2, 4) via vectors…

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Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.