-1 6. Let A = 10 0 1 1 3 1 -2 (a) Find the projection matrix onto the column space C(A).

Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Find an LUfactorization of the given matrix.

A: Given, To find LU factorization of the given matrix.

Q: Find an LUfactorization of the given matrix.

A: Let A=123456879. L and U are the lower triangle matrix and upper triangular matrix respectively. In…

Q: Factorize the matrix into LU decomposition. [0 5 41 A = 5 1 2 1 2 3.

A:

Q: An n x n matrix A is orthogonal if AA" = I. If A is orthogonal show that det(A) = ±1.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Use the first-order approximation to find the approximate inverse of the matrix [1.1 0.1 0] C = 0…

A: Given matrix 1.10.1001.9-0.10.204

Q: Suppose A = 2 a) is positive semi definite matrix then: a 10 O a Ja < 20 O b. a <-V20 O. lal < v20 O…

A: A positive semi definite matrix is the one whose eigen values are greater than or equal to zero. So,…

Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

A:

Q: Find x and y such that the rank of matrix A is 2. 1 0 a – 1 0 у- 2 г+1 -5 A = 4 x = Ex: 5 Ex: 5 С y…

A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

A:

Q: b) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s)…

A: Negative definite: A square matrix is said to be negative definite if all the eigenvalues of the…

Q: -2 0 2 ) Let A = Find an invertible matrix U such that UA = R %3D 1 2 3 is in reduced row-echelon…

A: We will use elementary row operation to get U.

Q: a b - Let B be a real matrix similar to a matrix A of the form -b a B = Q'AQ. How would you sketch…

A:

Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A:

Q: 8. Find the standard matrix for the orthogonal projections onto the column spaces of A 1 1 -1 –1 A…

A: orthogonal projection of column space of matrix A= A(ATA)−1AT

Q: 2. Find a nonzero vector that lies in the intersection of the plane {x + 2y + 3z = 0} 1 2 and the…

A:

Q: Find all a,ß>0 so that the matrix 3 2 B [4]= a 5 B 2 1 a is strictly diagonally dominant.

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Q: G4 : Find dịagonal matrix A that sotisfies a 16 o

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Q: Г1 3 2 5 1 [3 4 2

A:

Q: 0 0 1. Show that every matrix of the form A = |has an LU-factorization. Does it have an…

A:

Q: True or false? det(A) is defined only for a square matrix A.

A: True/False det(A) is defined only for a square matrix A

Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

A:

Q: Reduce the quadratic form x2+y²-9xy into a canonical form of the matrix.

A: The given equation is x2+y2-9xy. The standard equation is ax2+by2+cz2+2fyz+2gzx+2hxy. The…

Q: (4) Let B be the matrix 1 1 3 2 B = 2 3 4 -1 -3 1 -6 -2 and let TB : R4 → R³ be the linear…

A:

Q: 2 1 1 1 2 1 0 0 1 Jse Cayley-Hamilton theorem to find A20 where the matrix A =

A: A=211121001A-λI = 2-λ1112-λ1001-λ…

Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A:

Q: Q. No. 4 a) T: R2 → R² first performs a horizontal shear that transforms e2 into e2 – 2e1 and then…

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Q: (1 4 6 8 0 2 3 4 0 0 3 8 \0 0 0 4 Is the matrix A = singular? Why? Find A- if it exists.

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Q: 1 Find the real constants a and b in the matrix Q - a such that Q is orthogonal b

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Q: Consider the matrix 2 -3 -1 0 3 4 1 -2 0 -1 0 A = 1 -3 1 2 -2 -1 2 -6 2 4 -4 -2 (la) Find bases for…

A: We shall solve first question only with both the subparts . For others kindly post again by…

Q: Let M = -3 Find c and c2 such that M² +cqM+c»I½ =0, where I, is the identity 2 × 2 matrix and 0 is…

A:

Q: Which of the following is the LU-factorization of the matrix 1 0 a) Бая 0 1 0 -1] 1 1 0 b) :] 01 0 1…

A:

Q: P projects onto the C(A), then I- P projects onto D a. C(AT) O b. N(A) P. N(A") O d. I-Pis not a…

A: It is given that P projects onto the column space A, C(A).

Q: 1 a) Let A = 1 -1 %3D -1 1 (i) Compute the value of det(A). (ii) For what values of x will the…

A:

Q: 1) Let [2 1 1 -7] -1 1 A 3 1 0 0 7] Find the fundamental matrix for y'(t) = Ay(t).

A: Given A=211-70-10100310007

Q: 1 the Vector space P, of polynomials of degree at most two, the third column of the matrix of…

A: The given basis are: B= e1=4-x2,  e2=-2+3x2,  e3=1+x A= a1=1,  a2=x,  a3=x2

Q: The matrix H1, as any Householder matrix, has the form H1=l-2ww', for some vector w. The value of…

A: In order to apply the first step of QR-factorization to A, check for the first column of A. The…

Q: Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

A:

Q: Consider the matrix 3 0 - 2 A = 1 1 - 5 2 - 1 | d] Find the Condition Number K(A) USING INFINITY…

A: The condition number of a matrix, which is invertible, is defined as…

Q: 4. Let Q E Rxn be an orthogonal matrix. Show that ||Qx||2= ||||2 for %3D any x E R".

A: Given that  Q∈ℝn×n be an orthogonal matrix.

Q: Consider 1 A = 2 2 1 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A: We have to convert the matrix A=121213-1-34 into an upper triangular matrix U by using Gaussian…

Q: [1 2 2 5 1] Find the dimension of the column space of matrix A = | 0 %3D 0 0 0 0 0 dim(col(A)) =Ex:…

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Q: The matrix -| has a singular value decomposition A = UΣVT where U = and What is (Σ)11? Answer: हाज…

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Q: a b Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A:

Q: 2. Find the matrices P and D for an orthogonal diagonalization A=PDPT for 3 0 0 A=

A: First find eigenvalues eigenvactors corresponding to eigenvalues then we get matrices P and D.

Q: 3. Find LDU decomposition of the matrix [1 1 1] A = 2 4 3 3 7 6 (а) L 3D (b) D =, (c) U =,

A: Given: A=111243376To find: (a) L=?  (b) D=?   (c)  U=?