Find an algebraic description of the range of A by row reducing A^T and using the relation between R(A) and Row(A^T ) in order to obtain a basis of R(A).

Q: The product rule can be applied to the divergence of scalar f times vector    G-› as: ∇-›·(fG-›) =…

A:

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: Find a base for the line space of the matrix and determine the line rank.

A:

Q: Find an orthonormal basis for the colspace(A) when A = [1 1 -1 3 4 4 1 1 0]. Make sure that you show…

A:

Q: , find the orthogonal projection matrix on the subspace defined by the equation: 2х-у-3z-0.

A: a) Let v1 = [3,6,0] and v2 = [0,3,-1] be two vectors on the plane As we have 2(3)-6+3(0) = 6-6+0 =0…

Q: Use Gram-Schmidt process to transform the basis {(1, 1, 1), (0, 1, 1), (1, 2, 3)} into an…

A:

Q: Find a basis of the subspace of IR" defined by the equation 8ar1 - 7z2-4r3 0. { Basis:

A:

Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

A:

Q: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

A:

Q: Find a basis of the subspace ofRª defined by the equation 7x1+9x2+ 6x3 + 5x4 = 0. Basis:

A:

Q: Obtain an expression for a transformation matrix that will stretch a 3-D vector in x. Repeat for y.…

A: Let us consider an expression for a transformation matrix stretch a 3-D vector in x.  100→k00…

Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Find the characteristic polynomial of the matrix

A: In this question, we need to find the characteristic polynomial for the given matrix. p(x)=|A-x.I|=0

Q: Which one of the sets of vectors (given in Matlab notation) is linearly independent?

A: Note:  checking by matrix   if  zero vector is in the set then set is linearly independent

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

Q: Use Gram-Schmidt process to transform the basis {(1,1, 1), (0, 1, 1), (1, 2, 3)} into an orthonormal…

A: Given: Basis v1=1,1,1 , v2=0,1,1 , v2=1,2,3

Q: Project the first vector orthogonally into the line spanned by the second vector. 2 3 -2

A:

Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, -3, -4), (-2, –3, 2, -5), (1, 3, –2,…

A:

Q: Linear Algebra

A: According to the given information, it is required to construct an orthonormal basis of the set:

Q: Calculate the projection matrix of R3 onto the line spanned by (5, 1, −3)

A:

Q: Find an orthonormal basis for the subspace spanned by (0,1,2), (-1,0,1) and (-1,1,3).

A:

Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

A:

Q: Find an orthogonal and an orthonormal basis for 5 1 2 W = Span Spa { ·} 0 2 -2 -4 0

A: GRAM-SCHMIDT METHOD The Gram-Schmidt process (or procedure) is a sequence of operations that allow…

Q: find the characteristic polynomial of the matrix.

A: Topic-matrix

Q: orthonormal

A:

Q: If Pis the projection matrix onto the line through (C) (:) and then I - P projects onto the line…

A:

Q: 5. Find an orthonormal basis of the subspace spanned by the vectors 3. 1210

A:

Q: Find the singular value decomposition of the mat

A:

Q: Let Q be a symmetric positive matrix of order n, calculate the Fourier transform of exp{- (Qr, x},…

A: Consider Q to be a symmetric positive matrix of order n.

Q: Please explain how the chracteristic polynomial = -(lambda - 3)(lambda - 3)(lambda - 2) for the…

A:

Q: Please discuss your understanding of what a basis is for a vector space

A:

Q: 1. Find basis of Span

A:

Q: Create a vector-valued function whose graph is an ellipse, centered at (1, 2) with horizontal major…

A:

Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

A:

Q: Find an orthonormal basis of the plane x1 - 6x2 - x3 = 0. { }

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, –3, -2), (-2, –3, 2, –5), (1, 3, -2,…

A:

Q: Explain why we would apply the Arctan2 function to a homogenous transformation matrix ??

A:

Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

Q: Determine whether (1,1,1,1),(1,2,3,2),(2,5,6,4),(2,6,8,5) form a basis of R^4 (R). If not, find the…

A: Given set of vectors is  S=1, 1, 1, 1, 1, 2, 3, 2, 2, 5, 6, 4, 2, 6, 8, 5. We have to determine…

Q: Find the rotation matrix that could be used to rotate the vector by –20° about the origin. Take…

A: Here we have to find the rotation matrix that could be used to rotate the vector [1  1]' by -20°…

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

A:

Q: Find a basis of the subspace of R° defined by the equation 3x1 + 9x2 + 2x3 0. Basis:

A:

Q: Find the singular value decomposition of A

A:

Q: The set of all nxn matrices having trace equal to zero. is a subspace W of Mnxn(F). Find a basis for…

A:

Q: Find a basis of the subspace of R defined by the equation 3x1 – 7x2 + 6x3 0. Basis:

A: Evaluation of basis problem.....