Let u = [-1, 2, 2] and v = [1, -1, 1] Find (급x) O [3, 4, 1] [3, 4, -1] OI-1, 3, 4] O 14, 3, -1)

Q: What is translation that map each preimage to its image in (a) coordinate notations and (b) as a…

A: The image before dilation is referred to as the pre-image. After dilating with a dilation factor,…

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: 4. Add a vector to the set S {(1,0,0,00), (0,0,-2,0), (3,0,0,0). (0,9,0,0)} to make it span R* %3!

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Q: Select the orthogonal projection of (1,1,1) onto the span of (1,0,1) and (1,1, – 1) in R. O (2, 1,…

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Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: Find S ∩ T, (S ∩ T)c, Sc ∩ Tc, S ∪ T, (S ∪ T)c, and Sc ∪ Tc (1) S = (0, 1), T = [1/2, 3/2]

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Write v as a linear combination of u, u2, uz, where (a) v = (4, –9, 2), u = (1,2, –1), uz = (1,4,2),…

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Q: O vector startingfrom(6.3) to (e1) @ From (4, -7) to (-5-8) 3 From (3,o,1) to (-),3,o)

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Q: If vector u =(7,6) and v= (-3,5) then  Find u•v

A: Given ,  If vector  u = (7,6)  v = (-3,5)  We have to find dot product u•v

Q: Let u=(1,2,3) and v=(4,5,6). Then u and v are A. Pointing in the same direction B.Pointing in…

A: Let u=(1,2,3) and v=(4,5,6) When two vectors are in same direction then the angle between the…

Q: Prove that llu + v|| = llu - vll if and only if u and v are orthogonal.

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Q: Let u=(-1,2,-7) and v=(4,-8,28). Then v and u are A. Pointing in the same direction B.Pointing in…

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Q: Let L, be the line passing through the points Q-(-1, -3, 1) and Q-(3, 3,-1). Find a value of k so…

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Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

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Q: Which vector is collinear with [2, -3]? [2, -6] O [-4, 6] O(-2, -3] O [12, 18]

A: We have to find the vector

Q: If vectorAB =-7i + 3j + 8k and A is the point (-2, -3, 6), find B.

A: Given : AB =-7i + 3j + 8k and A=(-2, -3, 6)

Q: Let u= (-1, 1), v=(-3, 4), and W= (o, - 2). Find u - v + 4w

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Q: s= {(1,3,2),(-4,1,1),(-2,7,-3),(2,1,1)} and let U=span(S). what is dim U

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Q: find u ·v. u= [ 1,√2,√3, o],v= [ 4, -√2,0,-5]

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Q: Determine the projection of b = (2,1, –1) onto ā = (1,0, –2).

A: According to the given information, it is required to find the projection.

Q: Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly…

A: Solve the given problem.

Q: Let a = (– 3, – 1, 2) and b = (- 4, – 3, 2). Find the projection of b onto a. proj, b =

A: Use the projection formula for the given vector .

Q: Let u = (a, b, c) and v = (9, 10, 11). If u is parallel to (1,0, –1) and the proj along v is 10 202…

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Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: 1 Let u1 = 3 U2 = -1 , Uz = ,X = then write x as sum of two vectors -3 3 on in span {u1} and other…

A: Given, u1=1101 u2=-13-1-2 u3 = 101-1 x=1-1-33

Q: ) IH U = (1,2,3, - - 0), A = (2,4,6 .20), B = (1,3,5 . - 19) Verify Demargans laws

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

Q: Let u = (1, 2, 3) and v = (1, 2, -1). Find u- – u. v and v U - V = V - U =

A: Given u = (1,2,3) and v = (1,2,-1)

Q: 4) Find the adjoint of the operator Lu = u" + 4u'- 3u, where u'(0) = -4u(0), u(1) = -4u(1).

A: The objective is to find the adjoint of the operator, Lu=u''+4u'-3u where u'(0)=-4u(0), u'(1)=-4u(1)…

Q: Let a = (- 4, 3, – 2) and b = (- 1, 2, – 3). Find the projection of b onto ä. proją b > V

A: Answer:Given a→=<-4,3,-2>b→=<-1,2,-3>projection b→ onto a→ is given…

Q: Let a = (1, – 5, 3) and b = (– 5, 3, k). Find k so that ā and b will be orthogonal. k

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Q: Let à = (1, 1, 4) and b = (1, 2, - 5). of b onto a. - Find the projection proj- 6 = b =< -

A: For the given vectors the projection of b on a is given by

Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: д(х, у) Find the Jacobian of the Ə(u, v)

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Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

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Q: Show that the vectors v, = (0, 3, 1, -1); v, =(6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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Q: Suppose the vector ū =<3,1,-47 is translated so that it's heach is at the point C-1,2,3). where ito…

A: Given that the vector u→ = 3,1,-4 is translated such that its head is at the point (-1,2,3). We have…

Q: if u=(1,0,0) and v=(0,1,0), u and v are orthogonal Select one: True False

A: If dot product of two vector is zero then vectors are orthogonal

Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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

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Q: What are the components of the vector from P = (1, –1,1) to Q = (3, 2, 1) ? O (2, 3, 0) O (2, 0, 1)…

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Q: Find three numbers a1, a2, az to normalize the orthogonal set 1 in R³. aj = a2 = az =

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Q: Let u and v be u = [3,0,3] and v = [1,1,4]. Verify that: |u x vl? = |u]?\v]? – (u · v)²

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Q: Find three numbers a1, a2, az to normalize the orthogonal set 1 -2 a1 , a2 , аз 1 in R3. , az = = Ip

A: Here, a1 , a2 and a3 are unit vectors . w1 = (1,-1,3)  w2 = (-2,1,1)  w3 = (4,7,1)

Q: Let u = (-1,3)and v = (1, –1), then proj,u is: ) (1,1) ) (2,2) O (-1,1)

A: the projection of u onto v is given by projvu=u.vv2v substitute the values

Q: If vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1), what are the values of a, b, and c ?

A: Given : Vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1). That is

Q: the vector from P1(1, 3) to P2(4, –2) is

A: Given :

Q: Suppose {u,..., 4,, W1, ..., W,} is a linearly independent subset of V. Show that span (u;)…

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Q: Let L, be the line passing through the points Q, (5,-2, –3) and Q,-(-4, –11, 6). Find a value of k…

A: Equation of line in 3D

Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

Q: Let ä = (4, – 4, 0) and b = (- 1, 2, - 4). Find the projection of b onto a. proj, b = <

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.