9) Determine whether AMNO = AQRS. Explain. M(0,-1), N(-1,-4), 0(-4,-3), Q(3,-3), R(4,-4), S(3,3)

Q: Let u = (1, 2, 3), v = (4, 4, –2), and w = (6, 5, -5). Find z, where 2u + v - w + 3z = 0.

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Q: Find projvu.u = (−1, 3, 1), v = (4, 0, 5)

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Q: How to determine The direchon that the arrow at the pout 6,1) at he eghahión of he 1t arder g'=…

A: find the slope of the equation  at particular  point Example : y'=y-2x Take x=  0     0      0     0…

Q: b) Show that z, + z, = z, + Z, . 2

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Q: 4 as a linear combination of v,, V2, V3 when the coefficient of v3 is 1. 14 Write -4 Ov, + - (OV2+v3…

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Q: Find u · v. u = 8, 2 v = −7, 3 u · v =

A: A dot product is also called Scalar product , is a way of multiplying two vector quantities to…

Q: 3 10. Show that R² span

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Q: Find projvu.u = (0, −1, 2), v = (3, 2, 4)

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Q: Express the following as a linear combination of u =(3, 1, 7), v = (1, -1, 4) and w= (18, 7, 8).…

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Q: calculate the linear combinations. u = (−3, 1, 4), v = (6, −2, 8)

A: We have been given the vectors u = (−3, 1, 4), v = (6, −2, 8).

Q: 2. and as= Determine ifb=-1 =-2 is a linear combination ofaL az

A: Follow the procedure given below.

Q: 4. What value/s of c will make the set S = {(3, 5,-2), (3, c,-25), (1,–4, 7)} dependent?

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Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (4, 0, −3, 5), v = (0, 2, 5, 4)

A: Given a vectors,

Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: Express the following as linear combinations of 1= (2, 1, 4), v= (1, – 1, 3), and w= (3, 2, 5). 8.…

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Q: 6. Evaluate u x v, where u = -e, - 2e, + 2e,, v = 2e, - 2e, +e,.

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Q: 9. Let u AB and v = =PQ where A=(-4, 6), B = (3, 3), P = (4, 5) and Q = (-3, 8). Can you verify that…

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

Q: Let u= and v= identify 3u+v???

A: We have to identify 3u+v for the given vectors: u=2, -3 and v=4, -1. Finding 3u: 32, -3=6, -3

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

A: (b) ( 6, 11 , 6 )   We have to write it as linear combinations of (2 , 1 ,4 ) , (1, -1, 3 ) and (3…

Q: Let a = (4, – 5, – 4) and b = (4, 3, k). Find k so that ā and b will be orthogonal. k =

A:

Q: Q2: Suppose A = (0,2,4,6,8), B (1,3,5,7) and C (2,8,4). Find 1) AUB %3D 2) Ance 3) BnC 4) C\B

A: Given, A={0,2,4,6,8}, B={1,3,5,7} and C={2,8,4} To find, 1) A∪B 2) A∩Cc 3) B∪C 4) C\B

Q: 8. Express the following as linear combinations of u = (2, 1, 4), v= (1,–1, 3), and w= (3, 2, 5).…

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

Q: If v = (3, – 1, 1) and w = (-2, –2, –2) , what is v x w ?

A: Here two vectors v and w are given, we want to find the cross product or vector product of the given…

Q: Solve the following IBVP: UU+2, 0 0, u(0,t)=0, u(1,t)=-1, 120, u(x,0)=0, u(x,0)=1, 0≤x≤1.

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Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В %3 {3, 1, 9, e, а, с, 0}, and C 3D {2, с, 10, 9, 8, —4,…

A: solution of the given problem is below...

Q: 7-5{p}+3q7−5p+3q7, minus, 5, p, plus, 3, q when p=1p=1p, equals, 1 and q=7q=7q, equals, 7

A: We have to evaluate 7-5p+3q when given the values of p and q.

Q: Find projvu.u = (2, 3), v = (0, 4)

A: Given: Let the vector u and vector v be: Formula used:

Q: 7- Find a given that A(0, a)is equidistant from P(3, -3) and Q(-2,2).

A:

Q: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

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Q: Let a = (1, 3, 8) and b = (7, 3, 4). Compute 5a + 7b

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Q: If a figure is translated with the rule T⟨−3, 3⟩, which translation moves the image back to the…

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Q: The distance between u = (15, 7, 4, 6) and v = (3, 2, 1, 4) is 82 182 V182 O 48

A:

Q: Q2: Suppose A = (0,2,4,6,8), B = (1,3,5,7) and C= (2,8,4). Find 1) AUB %3D 2) Ance 3) Bnc 4) C\B

A: Given A = 0 , 2 , 4 , 6 , 8B = {1 , 3 , 5 , 7}C = {2 , 8 , 4} then (1) A∪B = {x : x∈A or x∈B}= {0 ,…

Q: 9. One-tailed alternatives are phrased in terms of: 00)2 2.0 n zlaarioqy C. # or = A. # B. D. < or…

A: According to one tailed test it is a test in which the critical area of the given distribution is…

Q: μ = 3, o² = 9, P(-6 < X<12) a. Determine P(u - ko < X <u+ ko) ≥ 1 − 1/k²

A: It is given that Mean = 3 And variance = 9

Q: how that Q(√2 + √3) =Q(√2,√3).

A:

Q: 51 3 -[---] -4 2 -2 Let u= (a) 5u-2v, 3 V= 5 W= -1 Find:

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Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (0, 4, 3, 4, 4), v = (6, 8, −3, 3, −5)

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Q: Let U%3D {а, с, е, h, m, о, р, s, t, и, у, 0, 1, -} А %3D {с, һ, о, р, s, и, e, y} B = {s, e, t} С…

A: The power set of a set S denoted by 2S is defined as the set of all subsets of the Set S including…

Q: 21, Referring to Example 50.9, show that G(Q&2, i/3)/Q(i 3) ~ (Za, +).

A:

Q: Let u= (4,15) and v=(2,-3,1). Then (2u+v).(u-3v) is equal to:

A: Given,    u=4, 1, 5, and v=2, -3, 1

Q: Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than…

A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove &lt;-…

Q: 3. Let, a, = 3, az = 4 and for n2 3, a, = 2a,-1+ an-2 + n² + 1, express a, in terms of n. %3D

A: Recurrence relation - it  is an equation that denotes  the nth term of a sequence as a function of…

Q: Express the GCD of (210,162) as a linear combination of 210 and 162.

A: Here, we have to find the GCD of (210, 162) as a linear combination of 210 and 162. For this, we…

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −3, −3), v = (3, −3, 3)

A: Given: u=(3, −3, −3), v=(3, −3, 3)

Q: Find projvu.u = (2, 4), v = (1, −5)

A: The projection of u onto v is denoted as projvu. The following formula is used to find projvu.…

Q: Given u = (-4,7) and v = (5,2), compute the following. Give your answer in the form . a. u + v =| b.…

A:

Q: 8. Express the following as linear combinations of u= (2, 1, 4), v= (1,–1, 3), and w (3, 2, 5). (a)…

A: Linear combination :  A vector v∈V(F) is said to be a linear combination of the vectors v1,v2,...,vn…

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В 3D {3, 1, 9, e, а, с, 0}, and С %3D {2, с, 10, 9, 8, —4,…

A: Using the definition of intersection, union and difference between two set

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.