If the vectors (y, x, i+ 2) and (x, 1 + y, –1) in C³ are orthogonal and if y + 9 -1, then the conjugate of æ is equal to 2+i(1+y) -2+i(1+g) –2+i(1+27) i(1+2y) O None of the given options is correct

Q: 1 If then C(A) contains all b2 3 b3 vectors b2 such that by .a O bz = 2b1 and bz = 3b; %3D %3D .b O…

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Q: First change the given pattern into a vector w of zeros and ones by turning each shaded square into…

A: Given w=1110 We have to find the M Let M=m1m2m3m4 Since, w=1110 then wT=1110

Q: Given x=(1,-2,-1,a) and y=(3,3,-2,1) are two 1x4 row vectors, where "a" is some constant, which of…

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Q: A. Calculate the first two vectors generated by the Jacobi method. -4 1 (-6) 1 3 -1 x ={-6 x(0) =…

A: To find- Calculate the first two vectors generated by the Jacobi method. -41013-10-15x = -6-67, x0 =…

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: 1. In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) | y >= O}…

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Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: If U, V,w are three vectors such that each is inclined at an angle of with the other two, and that…

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Q: 1 -1 6.5 [0] -2 10 7 3 x = 1 -4 10 -2 | 12.5] 3 3 10

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Q: If the vectors (y,x,i+2) and (x, 1+y,-1) in C are orthogonal and if y + y # -1, then the conjugate…

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Q: For the following three vectors, what is 2. Ć ·(3 Á × B )? В = 3.00î + 3.00ĵ – 4.00k B = - 3.00î +…

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Q: Consider the vectors in R 1 1 1 V2 =| 2 V3 = | 4 -1 1 Write the system, which corresponds to the…

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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: Find a least-square solution of Ax = b by finding orthogonal projection of b to ColA, where 1 4 A= 1…

A: Ax=bwhere,  A=1531-24   and   b=4-2-3orthogonal projectiona1=13-2 and a2=514 are column of A because…

Q: [1 3 1 For the matrixP = 0 1 1 find three different vectors that are not in the column space of P.…

A: Any vector which is not in column space must be in the null space. Null space of a matrix is   To…

Q: Find the value of k for which the vectors -4] -5 and -5 k are orthogonal. k =

A: Let the two vectors be- a →=-20-51        and  b→= -4-50k It is given that both the vectors are…

Q: 1 If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: X=(4, 1,0) B) No, because there is a free variable in the system of equations.

Q: 2 1 Find Q for the QR factorization of A = 0 -39 . given the orthogonal vectors -3 -13 -2 2 -6…

A: Given: A=2010-390-3-13-2 Also the orthogonal vectors are  v1=20-3, v2=-6-39-4, v3=-0.220.05-0.15

Q: The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and…

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Q: Find a value of k such that the given vectors are linearly dependent [ -2 4+ k 4 ,X2 = 2 X1= ,X3 =…

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Q: Consider the following vectors: -3 6 = | b2 || b3 where b1, b2 and b3 are any real numbers. Show…

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Q: If k is a real number, then the vectors (1, k), (k, k + 56) are linearly independent precisely when…

A: If k is a real number, then the vectors (1, k), (k, k +56) are linearly independent precisely when k…

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: B. Calculate the first two vectors generated by the Gauss-Seidel method. 1 1 -2] 1 10 4 x={ 15 x(0)…

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Q: . Prove that for any two vectors d and b in R³, there exist two vectors bí and b such that: T = 6 +…

A: The vectors a→ and b→ lie in the 3 dimesional axes.Any vector is a sume of two vectors.Thus,…

Q: verify that the given vectors are solutions of the given system. Then use the Wronskian to show that…

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Q: Find the value of k for which the vectors and 4 -4 are orthogonal. k =

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Q: If Q is an n × n orthogonal matrix and x and y are nonzero vectors in Rn, then how does the angle…

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Q: 5. Suppose vectors ū and i are linearly independent. Show that the vectors w = 2u+3ū and 7= ū+ū are…

A: if u and v are linearly independent then for au+bv=0 implies a=0 and b=0

Q: If the vectors (y, a, i+ 2) and (a, 1+ y,-1) in C are orthogonal and if y +y # -1, then the…

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

Q: 4 The vectors v = 3 and w = span a plane in R³. -28 -25 If the equation of this plane is ax + by + z…

A: Given: v=53-28 and w=45-25 spans a plane in ℝ3. To find: a and b, where the equation of plane is…

Q: Suppose v1,..., Vk are linearly independent vectors in R" (1 <k < n). Then the set Xk =…

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Q: be the set of all vectors of the form 4r – 6s – 6t | r + 3s – 15t - 11r + 7s + 8t 14r + 11s 6t with…

A: We have to solve given problem:

Q: 6. If X and Y are two row vectors. Use the array operations to find: 10 10 10 10 10 X, a) EX,Y; bb…

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Q: If A= (3/2) i –(½) j + k and B= i+j+2k, what is the value of A x B? Are the vectors orthogonal? O…

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Q: For which vectors (b₁,b2, b3) do these systems have a solution? X1 b₁ 1 1 1 X1 HO-N-HD-B b2 and 0 1…

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Q: Given x=(1,-2,-1,a) and y=(3,3,-2,1) are two 1x4 row vectors, where "a" is some constant, which of…

A: We are asked to find which statement is false.

Q: If the vectors ai + j+ k, i + bj + k and i +j+ ck (a # b ± c ± 1) are coplanar, then the value of…

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Q: 9. Given the bases B = {1+2t, 2+t} and C = {1-t, 2-3t) of P₁. Find the change of coordinates matrix…

A: As per the question we are given two different bases B, C of same polynomial space {1, t} And we…

Q: B.4 Find the orthogonal projection of the vector (1,2..n) on the orthogonal complement M- of M in E…

A: The complete solutions are given below

Q: Find the value of k for which the vectors -5 -1 4 and -4 k are orthogonal. k =

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Q: Consider for this question the four vectors X= 3 w =0 (a) Compute x + 2y, \y], and the angle between…

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Q: We have the given matrix M such that M = [4 5 p 5 4 q 0 5 r] We know that the two vectors (4, 5,…

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Q: Given the following vectors, - 1 3 Determine whether the vectors are independent of each other or…

A: Linear Independence :  A set of vectors v1,v2,...,vn is linearly independent if…

Q: Suppose that u = – 2i – 5j and v = - 3i – Compute the given linear combination of these two vectors.…

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Q: 3) S contains only the vectors (-2+x-x² - 2x³), (4 + x - x² + 2x³), (8 + 5x -5x²+2x³), (10 + 7x -…

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Q: -- -4 1 -3 For A = -2 find the orthogonal vectors vị, V2 and v3 to be used in constructing the 3…

A: Given matrix is: A=-41-302-2003

Q: 3. Consider the following vectors: ä=7-2] +3k, b=27-3k, and a = -37 +2j. Compute the required…

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Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is -…

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