find the inuerse matrix of motrix 1 2.Use +he Laploce expan si on of the column. 4 0 1 6 0 3

Q: Let a Consicler the matrix 121 4) S23. A=/S. 87.3 Find Miz, Ci2 and M2z Czt

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Q: Q3: What 3*3 matrix that will generate Figure2 from Figurel. (1,21 LIRAQIA UC2S)ERSITY (2,5) 2,2)…

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Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4. A = -4 -3 L U

A: We have to find L and U matrix.

Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: 5.)Write the aua mented matrix for the syshem X, +2X,-X, tXc =l =マ+ t bulo

A: We have to solve given problem:

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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…

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Q: 4. Find the cofactor matrix for the matrix. 5 9 1 8 5 6 4

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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.…

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Q: Find a 2 x 2 matrix B + 0 and B + 1, such that AB = BA, where A How many such matri- 2 ces B are…

A: Given data: The matrix is given by "A". A=1221 Consider the matrix "B". B=abcd According to the…

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A: Let the genral 6*6 matrix is given by…

Q: Let A be an n × n matrix and let D be an n × n diagonal matrix. (a) Show that D = (d11e1, d22e2, . .…

A: (a) The diagonal matrix D is of the form

Q: Examine the nature of the following matrix defined by A = [0        1 + 2i       −1 + 2i      0  ]…

A: Given:  A=01+2i−1+2i0 To explain nature of above matrix and to find its proper values and proper…

Q: 8. For the column matrix v=(v₁) we have explain then: (VA); =Vkaki

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Q: 4 x 4 matrix A [aij ] whose entries satisfy the stated condition a=i+j %3D

A: We have to find out the matrix 'A' of order 4×4 and the given condition is aij=i+j.

Q: Determine the Householder matrix that annihilates all but the first entry of the vector v = [2 22…

A: Let α=2222T Then take, v=α-αc1=2222-α2000=2222-α000 ,Here α=±||a||2=±2 Now , since,α1  is positive ,…

Q: Let A be an n × n matrix and let B = A + I. Is it possible for A and B to be similar? Explain.

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Q: (b) Explain why in general, if u = [u uz] is a row of length 2, A = a1,1 a1,2 [@2,1 @2,2] we always…

A: Answer

Q: Find an SVD of the matrix. 7 1 A = 0 0 4 8 Give an SVD of matrix A below. A =

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Q: (a) Find the matrix A so that AB=C, where а, а, а, B= b, b, b, & C= b, b, b, a, az az (2 rows are…

A: Given B=a1a2a3b1b2b3c1c2c3 now using row operation R1↔R3 ~c1c2c3b1b2b3a1a2a3

Q: Find the coordinate matrix of x relative to the orthonorm x = (10, 20, 5), B = {(÷, 0). (- ÷ [x]B =…

A:

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

A: If A is an invertible qxn matrix with orthonormal columns & W be the column space, then the…

Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

Q: suppose A be any Hew of have symmetric matoir order and this matrix 4x4 rank of 3 the caleulata the…

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Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

Q: i. Let A, B; 3x3 order square matrixes, Meets the conditions BA=A3 & A3 – 2AB = 1 Prove that A is…

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Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: Find an SVD of the matrix. 5 1 A= 0 0 2 2 Give an SVD of matrix A below. 2/5 V5 3/10 V10 5 10 10 A =…

A: Let us find the Singular Value Decomposition of the given matrix in the following steps.

Q: Let A be 3 x3 R given matrix by over 2. A = -1 Using the result of A find the value (s) of makes the…

A:

Q: Matrix with rank A= 4 het A be a 5x6 ind cim Row A, dim Col A, dim Nul A, din Bow AT, dim Cal AT,…

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Q: Let  A be a symmetric tridiagonal matrix (i.e., A is symmetric and aij = 0 when ever |i−j| > 1). Let…

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Q: What matrix E puts the matrix A into an upper tr 4= U? Show your work! 210 042 A =

A: Introduction: In linear algebra, LU Decomposition, also known as lower–upper (LU) decomposition or…

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Q: Find Hessicn matrix ? 2.

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Q: 1 if k = i and l = j if k = j and l = i if k = l but k # i, j 1 (Si3)ke = 1 otherwise.

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Q: d the third column of A 'without computi 1 be found without computing the other om nted matrix (A…

A: The matrix is given as A=-2-3-2525431218. To determine the third column of A-1 without computing the…

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 A = - 4 3 L = U =

A: Given that, A = LU

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A: Given matrix is, A=23-110302-3-213 To find the elementary matrix A that as a post multiplier of A…

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A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: A be square matrix. I f A"= Onva for %3D n> 2. Then A= Onen

A: Suppose A be any square matrix of order n such that An=On×n     for n>2

Q: Q3/create a matrix A and 1- add fourth & fifth rows equal to [1 2 3] by using [1 2 3] A= 4 5 6 L7 8…

A: Here is the solution:

Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

A: In the given question, the matrix A is given as: A=248039007D=diagA=200030007

Q: {(: ;) :*vez} : х, у Є Z y Let T' = Under the usual matrix operations of addition and…

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Q: 口 WLJ 18) Which is the product of the matrix? [21 4] x L2] 13 O (8] 41 8 O (6] O [13]

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Q: y: Date: / / Rousl column reduce the given mahrive matrix into EF and locate the pirot position. -3…

A: We first calculate reduce row echelon form And then denote first non zero entry of each row , that…

Q: Solve for the matrix X if AX(D+ BX) = C. Assume that all matrices are n x n and invertible as…

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Q: Find the inuerse matrix of motrix 1 2.U se the Laplace expansi on Of the column. 13 401 6 0 3

A: Given matrix is 813401603 find the inverse of matrix

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.