Q3) Consider the relation R = {(1,3), (1,4), (3, 2), (3, 3), (3, 4)} on A = {1,2, 3, 4} a) Find the matrix M, of R. b) Draw the directed graph of R.

Q: b) Determine the matrix A for the linear transtormation which means that the vectors Of the room are…

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Q: Let A = [aj be a 4 x 4 matrix. Develop the general expression for det(A).

A: Given:               Matrix A is : [aij] is the 4×4 matrix;   General expression for the determinant…

Q: Find the Projection Matrix

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Q: Compute the product 0 () 0 (²) as a 2 x 2 matrix. What kind of isometry is this product?

A: Given product is  Oπ5O2π15 where Oθ represents rotation matrix through an angle θ in anti-clockwise…

Q: Using only 0's and l's, list all possible 2 × 2 matrices in row canonical fom.

A: Row canonical matrix All zero rows, if any, are at the bottom of the matrix. Each leading non zero…

Q: Let {v1, v2, ..., vn} be an orthogonal set in R" with respect to the Euclidean inner product. Let A…

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Q: Find the adjacency matrices for the directed graphs in (a) and (b). (a) V3 V1 V2 For the adjacency…

A: Rematch: The given graphs in (a) and (b) are not diagraphs (because no edges are directed with…

Q: 4. Verify that M, = 1- Px = 1- X(X'X)-X' is symmetric and idempotent for any matrix X, where I is a…

A: A matrix A is symmetric if

Q: Let U(-5, -4, 3, 4, 6), V(-4, 1, 7, 1, 0). Find the inner product U.V

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Q: Let A be an n ×n matrix. Prove that dim(span({In,A,A2, . . .})) ≤n.

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Q: 3. Show that the hat matrix is symmetric and idempotent. (That is, show that H' = H and that НН -…

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Q: Let I be the rdentity of nxn. Please Compute 3. matrix the matrix funct ions CosT I (i²=-1)

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Q: 6. Prove that ||4| , 14. , |4. are matrix norms.

A: This is the problem of functional analysis.

Q: I, explain why BTB must be symmetric for any n × m matrix B. (If yo

A: We will prove that the matrix Is symmetric as following.

Q: Findthe Linear Eransfromation whose matrix MT with regard to the base to mec2And the natural ruleto…

A: Given T:C2→C3 be a linear transformation whose corresponding matrix is given  MT=i-i1+i-21-1+2i and…

Q: a() – 4 (6) - (1) - (-) - Find a 2 x 2 matrix A such that A

A: We have to find a 2 × 2 matrix A such that A12=A23=41 Let the matrix A = abcd

Q: If the rows of an n X n matrix A are linearly inde­pendent as vectors in Rn, what is the rank of A?…

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Q: 3) Let B, = {u,, u2} and B2 = {v,, v3} be the bases for R° in which u, = (1,2), uz= (2, 3), v =…

A: The solution is given as

Q: Let D be a linear transformation from R to R", and suppose the null space of the matrix for D has…

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Q: Find Jordan form of this matrix

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

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Q: Find a numbert such that (3,1,4), (2,–3,5), (5,9, t) is linearly dependent in R³.

A: A set of vectors is said to be linearly dependent, if there is a nontrivial linear combination of…

Q: Let T be the triangle with vertices (1, 1), (−3, −3), and(2, −1). Find the coordinates of the…

A: Given, Let T be the triangle with vertices (1, 1), (−3, −3), and (2, −1). f(v)=4-3-42v

Q: Find A and a- basis for which the system reduces to ú: lu+ v and i = av

A: We have to find the value of λ and a basis for which the system reduces to  u·=λu+vv·=λv

Q: 5. Use the matrix o Rotate polygom ABCD with coordinates A(0, 0), B(4, 1), C(S, -1), and D(-2,-3) -1…

A: Given A(0,0) B(4,1) C(5,-1) D(-2,-3)

Q: 2. Determine the matrix X, such that:

A: Solution:-

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

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Q: FIND THE FUNDAMENTAL MATRIX AS W ELL AS THE FUNDAMENTAL MATRIX SATISFYING )- I x'= -4 %3D

A: For the solution follow the next steps.

Q: For an undirected graph G, show that the result of the matrix-vector product A(G)1 (where 1 is a…

A: Let AG be the adjacency matrix of G andAGij=aijThen note that AG 1 is an column vector and…

Q: 5 Aaron and Maya want to write the vector u = -5 as a linear comb -19 -2 1 V1 -2 V2 = 1 and V3 = 2…

A: The { v1 ,v2 ,v3 } is not a set of orthogonal vectors.

Q: 2. Use matrix multiplication to find the orthogonal projection of (1, 2, - 3) onto the a. ху-plane.…

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Q: The parts (a) and (b) of this problem are independent of each other. G1 G2 (a) Prove that the graphs…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Notations That Represent A Line

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Q: Explain transpose AT of the m x n matrix A?

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Q: Without using determinants, show that {(2, –x,,3x²,x³} is a basis for Ps then find dimension for P3

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Q: Prove that ||A||₁, ||A||, || A||₂, are matrix norms.

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Q: Find the transition matrix from the ordered basis of 3 R? to the ordered basis of R?.

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

A: I have checked one by one option wise

Q: Let A = {2, 3, 4, 5, 6}, B = {11, 12, 13, 14, 15} and define the relation R from A to B by aRb if…

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Q: Find the matrix P that multiplies (x, y, z) to give (y, z, x). Find the matrix Q that multiplies (y,…

A: The matrix “P” will be, P=010001100  if multiplies (x,y,z) to give (y,z,x) Explanation:…

Q: Prove that deleting the last column of an echelon form (respectively, the row canonical form) of an…

A: Echelon matrices come in two forms: the row echelon form (ref) and the reduced row echelon form…

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

A: The given vector space is Mm×nZ2.

Q: Suppose that {v1, v2,..., vn} is a linearly independent set of vectors in Rn. Show that if A is an n…

A: Let's suppose we have a linear relation:…

Q: Let A be a matrix and mathbfb be a matrix and a vector defined by 1 -1 b : 1 3 Compute x* that…

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Q: Suppose A is nxn mabrix Cequre mabria) prove that if the pivobe for the matrix is Unique ornoto…

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Q: Compute the determinants in by colactor expansions. At each step, choose a row or column that…

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Q: 3) Develop matrix form of the quadratic spline polynorhials for these data po: (1, 1), (2, 3), (3,…

A: Given: 1,1,2,3,3,5,4,2 n=4

Q: Determine whether the matrix is invertible. 5 5 -5 8 2 -8 -7 0 7 Also find AT

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Q: Compute the determinants in by colactor expansions. At each step, choose a row or column that…

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Q: Use powers of adjacency matrices to determine the number ofpaths of the specified length between the…

A: Here's the given (5 x 5) matrix A A=0001100011000111110011100so as we have to find the length of…