Suppose that u = (0, b) is a non-zero vector in R?. Show that the line L = Span({ủ}) has Cartesian equation x = conclusion ifú = (a, 0) is a non-zero vector in R2. 0. In other words, L is the y-axis. State and prove a similar

Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Introduction: The coordinate of a point x,y,z is actually the components of the position vector…

Q: onow that the v ectors 2 3 do not span R' by giving a vector not in their span.

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A: The detailed solution is as follows below:

Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

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A: Consider the given point as, P11,-2,1 and P2-1,3,0

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A: We can evaluate  the given problem as follows:

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

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Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

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A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

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Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

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A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

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Q: Find a vector in the plane parallel to the line ax + by = c.

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Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: Let x 0 and y 0. (a) If xly, show that {x, y} is a linearly independ- ent set. (b) Extend the result…

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Q: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

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Q: Show that the vector v = ai + bj is perpendicular to the line

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Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given that L is a line in 2-space or 3-space that passes through the points A and B then the…

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A: Find the slope of the given vector v=ai+ bj is given by ba.

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A: The transpose component is X=1, -3t

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Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

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Q: Show that the vectors do not span R' by giving a vector not in their span.

A: Solution :-

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Q: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

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Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

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Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

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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.