Find the matrix A' for T relative to the basis B'. T: R3 R3, T(x, у, 2) %3 (у + z, х — 2, х + у), В' %3D {(5, 0, —1), (-3, 2, —1), (4, —6, 5)} 48/5 -14/5 -7/2 159/5 -41/5 -19/2 A' = 56/5 |-12/5 -3

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

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Q: Find the coordinate matrix of w relative to the orthonormal basis B in Rn.

A: Let,

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Q: a) What is the transition matrix PT<S from the S- basis to the T-basis? b) Find the coordinate…

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Q: I want to know about change of basis matrix and what does it mean by diagonalization of a matrix.

A: Change of Basis:

Q: Derive a composite matrix that transforms a square ABCD with coordinates A(0,0), B(1,0), C(1,1),…

A: As per the question we have to find the affine transform which will transform the points A,B,C,D…

Q: find the transition matrixcorresponding to the change of basis from {u1, u2} to {e1, e2}. u1 = (1,…

A: u1= (1,1)T,      u2 = (-1,1)T Let e1=(1,0) e2=(0,1) We now need to express u1 and u2 as linear…

Q: Answer considering the matrix with the given vectors as its columns

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Q: Suppose that a 3×3 matrix A has three columns C1, C2, C3 which span the plane given by x + 2y – 5z =…

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Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

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Q: 7. Find a 2 x 2 matrix that reflects vectors in the (x, y) plane across the x axis. 8. Find a 2× 2…

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Q: Find an orthogonal basis for the column space of the matrix to the right. -1 2 -8 4 1 -2 7 1 - 4 - 3

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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 coordinate matrix of x = (1, 2, −1) in R3 relative to the (nonstandard) basisB′ = {u1, u2,…

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Q: 14. Find the standard matrix that performs the clockwise rotation of vectors in R² about the origin…

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A: Let us consider  3×1 matrix  n=xyz and we have given [ ]x be the skew symmetric matrix…

Q: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

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Q: Construct a matrix A E M22(R) so that the solution set of the homogeneous equation Ar = 0 is a line…

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Q: What will happen if the Gram–Schmidt process is applied to a set of linearly dependent vectors {v1,…

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Q: Linear Algebra

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

Q: 2. Diagonalize the matrix using normalized vectors. B= 3 1

A: Given,        B=1331

Q: 1 3 1 -1 2 0 5 -2 6 1 A = 3 -1 3 4 1 -3 -2 3

A: We have to find the Nul(A).

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A: Given: Here it is given an n×n matrix of Ms whose jth row is Vj as well as an n×n matrix MT whose…

Q: If {u1, u2, U3, ... set of vectors in R" and the matrix U has columns u1, ..., Uk, then U'U is the…

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

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Q: 1 -1] 5 -4 2 1 -3 1 -2 -1 3 2 16

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Q: stable

A:

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Q: How many matrices are there in the vector space Mmxn(Z2)?

A: The given vector space is Mm×nZ2.

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Q: Find the basis of column space of the matrix A given in the attached image .Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1,…

Q: Find an orthonormal basis spanned by a set of vectors V1 = (2, 2, 1), V2 = (−2, 1, 2), V3 = (9, 0,…

A: We will first find orthogonal basis using Gram-Schmidt Process, then orthonormal basis

Q: Find the stable vector of this Matrix:  0 0 1 0 1/2 1/2 1/3 2/3 0

A: A stable vector is a probability vector such that PW=W.Let W=xyz. Then, we have 0010121213230xyz=xyz…

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.