27 Let L be the line in R³ that consists of all scalar multiples of the vector 2 Find the reflection of the vector a = 8 in the line Reflf(v) =

Q: 9

A: We need to determine all the values of the constant a for which the vectors

Q: 4. Let u = and w = . Find the resultant vector 4u + 5w.

A: We will find the resultant vector.

Q: For a vector b = (-2, 1, –2) and a plane P : 3r – 2y – 4z = 0 (a) Compute a basis of P. (b) Compute…

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Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: Let x, y, and z be vectors in Cn and let a and B be complex scalars. Show that a ( z, x) +B ( z,y )…

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Q: Let L be the line through the point Q=(−3, 3, −2) and direction vector d=[4, 5, 1]T. Find scalar…

A: We need to find equation of planes.

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: Let L be the line in R³ that consists of all scalar multiples of the vector 2 Find the reflection of…

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Q: A, B, and C are 3 distinct points with non-zero position vectors a, b, and e respectively. a If a x…

A: Given three distinct points are A, B, C. with position vectors a, b, c respectively.…

Q: Г10] Let ÿ = 7 and i = -2. Write y as the sum of two orthogonal vectors, j1 parallel to u and j,…

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Q: find all values of the scalar k for which th e two vectors are orthogonal.

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Q: Let x and y be vectors in the R³. Suppose that x is a scalar product of 2 and the vector y. Prove…

A: x and y are vector in R3, x is scalar or dot product of 2 and y vector,  it means x = 2.y,

Q: (2) Find the real values of a,b.c that make the convolution equal to zero for the vector function…

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Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

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Q: Let u = [-1 3 -1] and v =[-6 0 5]. Find the vector w = 2u – 7v and its additive inverse. %3D

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Q: Let V=R^2 and let H be the subset of V of all points on the line 2x+3y=6. does H contain the zero…

A: Given  V=R2 and let H be the subset of V of all points on the line 2x+3y=6.

Q: Let v = i - 5j and w = -2i + 7j. Find the specified vector or scalar 6v - 3w.

A: We plug v = i - 5j and w = -2i + 7j in 6v - 3w. 6v-3w=6(i-5j)-3(-2i+7j)=6i-30j+6i-21j=12i-51j

Q: 4. Define the function T: R² → R as 1 T(v) = Av = |-2 4 V2 %3D -2 a. Find T(2, 4). b. Find the…

A: We need to find pre image.

Q: Consider the following. u = -8i – 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. -3j – 3k…

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Q: -2 [5a] Find the value of a such that the vectors u =a +4 and v = |2 are orthogonal.

A: Please refer the attached image for complete solution. Given: u = -2a+4   1  & v = 5a 2 0 are…

Q: #f(r) +7z +2, g(x) -r+1 find a degree 2 polynomial h(z) such that together these 3 are linearly…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: -2 Let L be the line in R' that consists of all scalar multiples of the vector Find the orthogonal…

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Q: Let L be the line in R3 that consists of all scalar multiples of the vector 1 Find the reflection of…

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Show that the vector form (x, y, z) = (-5, 1,0) + t(3,2, 1) for some parameter t ER satisfies the…

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 3w + 2v.

A: Given: u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

Q: Let T: R³ → R³ be the orthogonal projection onto the line L in R3 containing all scalar multiples of…

A: The formula for orthogonal projection of x→on v → is given by.projv(x)=v.x||v||v→since T:R3→1R3and h…

Q: 3. Find a. the vector component of F = 10 āz – 6ā, + 5a, that is parallel to G = 0.1 a, + 0.2ā, +…

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Q: Make all obvious simplifications.

A: We have to solve

Q: Consider the following. u = -7i - 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. i- 3j -…

A: Given, u=-7i-2j-4k v=4j+4k We know that projection of u on v is…

Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

A: Note:  part(b) is the independent subpart of part(a) and also it is incomplete. so part (b) can't be…

Q: let v =〈−2, 5〉and w =〈3, −2〉. Find a scalar α such that ||v + αw|| = 6.

A: Given, v=-2, 5w=3, -22

Q: 5x – 3y – 13 = 0 is a scalar equation for a line in 2-space. a) State 2 points that are on the line.

A: Given: the equation of straight line  5x-3y-13=0                 Answer a) all the points which are…

Q: Consider the following. u = -9i - 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. -3j – 3k…

A: The given vectors,u=-9i-2j-4k, v=4j+4k

Q: Let L be the line in R³ that consists of all scalar multiples of the vector -21. Find the reflection…

A: The solution is given as

Q: -) Find the vector form F(t) = ro + tu of the line through the points P(2, 7, 5) and Q(7,8, 12) Find…

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Q: Let a = (5, 4) and b = (1, –5). Show that there are scalars s and t so that sa + tb = (-13,-22) You…

A: Given, Let a=5,4,b=1,-5 And sa+tb=-13,-22

Q: 26. Find a unit vector whose representations are perpendicular to the plane containing PQ and PR if…

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Q: 10. Consider the plane 2x - 3y+4z 0. Find a basis B of this plane such that (B = for ū =

A: Solution:-

Q: (1) Let x and y be the vectors -- -- -) x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z…

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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: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

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Q: 2. Determine all real numbers x e R for which the vectors (x, 0, 1), (2, x, 3), and (4, 5, 6) ar…

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Q: 3. Use the Wronskian to determine whether the functions f1 = e*, f2 = sinx and f3 = x³ are linearly…

A: The Wronskian approach helps to find whether the given functions are linearly dependent or not. If…

Q: Suppose that ū and i are vectors satisfying ủ ở = p , ||ủ|| = q , and 3 =. Find the angle (in…

A: (a) Consider the values for p, q and r and the values for the vector u, v and dot product for u and…

Q: 1 Find the domain of the vector function r(f) = 4ti+ %3D t-2J O (0, 4)U(4, ) O (o, 2)U(2, ) O…

A: The domain of vector function is all values of t for which its each component function is defined…

Q: Let T : R → R³ be the orthogonal projection onto the line L in R3 containing all scalar multiples of…

A: Given scalar multiple of the vector -101

Q: 5) Find the scalar and vector projections of b onto a. a = 5i – k, b= i + 2j + 3k %3D -

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.