a) Let U be an m xn matrix with orthonormal columns, and x and y be in R". Then I Ux I=I x| (Ux) (Uy) = x y i. (Ux) (Uy) = 0 if and only if x y = 0.

Q: if A is (m*n) matrix, prove 'rank(A)=n-dim(N(A))

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Q: Let {v₁,...Vn} R" be linearly independnt. (a) Let A be a singular n × n matrix. Prove or disprove…

A: Let a set of vectors be For m scalars  satisfyIf the only solution is Then the vectors  are linearly…

Q: Let A be square matrix. If A" = 0. A= Oava %3D for n> 2. Then

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Q: How is the matrix of R^−1 obtained from that of R in general, that is, when A = {a1, . . . , am}, B…

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Q: 10. Let A E R"Xn be an upper triangular matrix, and let B = A¡j for some i, j. (a) (BH) Show that if…

A: Upper triangular matrix: A matrix of order n×n is said to be upper triangular matrix if each element…

Q: Consider the BVP u" =u+2,0<t<1, u(0) =1. u(1) = -1 Using the central difference quotient and 4…

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Q: Determine and explain if it is true or false Let A=(a) such that a a non-singular matrix (det =…

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Q: (BH) Consider the following matrix in R5×5. * 0 0 0 0 0 0 0 0 0 * A = * * * where the *s are…

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Q: If A is an q x n matrix with orthonormal columns & W be the column space, then AA"y Projwy for all y…

A: Given that A is a q×n matrix with orthonormal columns. Hence there are q rows and n columns in A.…

Q: Suppose that you have the following model and data to estimate the following equation Nobs Y X2 X3 1…

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Q: = (3, 6) 2. It is known that u = (-2,3) and v = relative to the inner product in R? which is derived…

A: 2 Given that u=−2,3 and v=3,6 And A=2134. We have to find the u and v. We know that…

Q: s elect the matrix correspon ding to the form QLX,, Xz, Xx, Xu ) = - 2x1²+ 5 X; - 7×3 -4 Xú - 6Xi Xz…

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Q: 4. Let X'= (X₁,..., Xn) be an n-dimensional random vector whose covariance matrix exists. Let A be…

A: Let's simplify Covariance of AX,  Cov(Ax)= E[(Ax-E(Ax))(Ax-E(Ax))]' = E[(Ax-A*E(x))(Ax-A*E(x))]'

Q: Let T: R³ R² be defined by T → Let B3 = 6 ----A-D-A---M--N} and C 5 {" (6) - L U₂ -3x1 3x2 + x3 7 {…

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Q: 14. Let v(1,2), va- (2,3) and let 5= matrix from (w), wy) to (v₁, v₂) (a) w₁(1,5) and wa-(9,4) (b)w,…

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Q: Generate the matrix A of order n= 100, whose generic element is a; = sin(max(i, j)) The condition…

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Q: Let A be 3x5 matrix. Then AX=b has always infinitly many solutions.

A: Since not a particular question asked ,as per guidelines solution to first question is given below

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: Let A = [ 0.7 3 ²] 0.2 0 and u = [80, 30]¹.

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Consider the matrix distributive property. (c + d)A = CA + dA, where A is a matrix and c and d are…

A: Given Property is (c+d)A=cA+dA where A is matrix and c and d are scalarsGiven A=[aij]We know that…

Q: 27. Let A be square n x n-matrix. Show that A + AT is symmetric. Show that A+ ATY X. Ax = x X for…

A: Given  is a square matrix of order  .To show that matrix  is a symmetric matrix.And to show  for all…

Q: Show that if the non-zero vectors s(1), s(2),..., s(m) are conjugate to a positive definite matrix…

A: We are given that the non-zero vectors s(1), s(2), ..., s(n) are conjugate to a positive definite…

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: 4. Let martix A is any (mxn) matrix and let B is a square matrix. Show that, any vector 'b' chosen…

A: Given: Matrix A is (MxN) Matrix B is square and diagonal matrix Vector B is coloumn space of matrix…

Q: * Proferties of Deta If (Alis a square matrix for eXamlle A=

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Q: Show that f(x): Rn -->R is a convex function f(x)=max{ ||APx-b|| , P is a Permutation matrix}…

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Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

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Q: Express the model Y₁ = Bo + Bixi + B₁r? + &i where the ɛ; have mean zero, variance o² and are…

A: Given Yi=β0+β1xi+β11xi2+εi ,i=1,2,......5

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.