et X = {(x,y, z): Vx² + y² + z² <1} be a subspace R° with the standard topology and 0 = (0,0,0). Show that the fundamental gro

Q: Is Mmxn(Q) is a vector space over R?

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Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Let pu: R³ → U be the orthogonal projection onto the subspace U = {(x, y, z) = R³: x-y-z=0}.…

A: Introduction: To find a linear variety S' that projects onto S under the orthogonal projection pu,…

Q: The curd of the vector funchion v = Jx i+ Jgj+ ZK is ☺ xi+ yj+ zK

A: It is given that, v→=x i^+y j^+z k^   According to curl, the swirl of a vector around a point. It is…

Q: 6x 1 = (2)ų pue 3 – x = (2)6 hq pelves as a co to on to a los e os (26) = projy (f) Use the inner…

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Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

Q: Define the following subset of R3 x1 E R³ : a'x= 0 = < x = x3 where a' = [-1,1,4]. Show that W is a…

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Q: W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space,…

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Q: Show that U = {(x, y, z)|x – 2y − z = 0} is a subspace of R³.

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Q: What is the dimension of the vector space ab c S= { EM2x (R): a =b=c} de f

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Q: Let V ((x,y): x 20) with standard operation on R2. Is V a vector space?

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Q: Let f(x,y, z) = a² + 2y² +z² and g(x,y,z)=z-xy. Find a unit vector u satisfying D.f (1.1,2)= 0 = D,…

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Q: If the vector K az+Lay+ Ma, shows the maximum increase rate and direction of the scalar V at point…

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Q: Determine whether U = {(1, s, t)ls,t e R} is a subspace of R.

A: FOR ANY SUBSET U TO BE A SUBSPACE OF ANY VECTOR SPACE V IT IS NECESSARY THAT U HAS ZERO VECTOR IN…

Q: Consider the vectors v1, v2, ..., Um in R". Is span (01,..., īm) necessarily a subspace of R" ?…

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Q: Let V = {(x, y): x 20} with standard operation on R2. Is V a vector space?

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Q: Suppose that diastolic blood pressure readings of adult males have a bell-shaped distribution with a…

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Q: Let V = {(x,y) where y= 3x+1 x ER} with scalar multiplication defined by k(x,y)=(kx,y) is a vector…

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Q: Is W = ((x,y) | xy=0} a subspace of R??

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Q: Don't change the W subspace. It is  W = {(x,-x, 2x): x, y ≤ R}

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Q: (x, y, z) = ( i i

A: Given that Length of vector = 6√3 We have to find component of vector.

Q: b) The tangent subspace Wp at p ES is the plane through 0 with normal vector p. Find an explicit…

A: b) The tangent subspace at a point p on the unit sphere is the plane through the origin with normal…

Q: Show that U = {Ae² sin(3x): A = R} is a subspace of V.

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Q: Let W = {(a, b, c, d) E R*| a – b = 0,2b + c = d}. i. Show that W is a subspace of R*. ii. Find a…

A: We will prove the following result.

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.