What is the result of this matrix multiplication? OA –13] 19 OB. -18 OD. 181

Q: 1. Identify the two-by-two matrix with matrix elements a;; = ij. %3D 1 4 4 2 4. O (1 4.

A: NOTE: Refresh your page if you can't see any equations. . there are 4 elements in the 2*2 matrix,

Q: Find the elementary matrix E such that EB = A where %3D 2 3 1 2 3 1 A = 4 -3 -2 and B = -8 6 4 7 -6…

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Q: Find the elementary matrix E such that EB = A where %3D 5 4 1 ] 4 1 A = |4 |7 -6 1 -1 and B = |12 3…

A: EB=A multiplying with B-1 on both sidesEBB-1=AB-1E=AB-1

Q: 1) Construct the matrix A =(a;;) where 3x2 ) aj = i+j, if i = j,and Li-j, if itj %3D

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Q: 4. If det(Adj(A)) = then what is det (A-1) if A is a (4 × 4) matrix?

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Q: 10 C.

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Q: . Given the matrix A below, alue for det in A A = 1 0 2 2 0 0 2 1 1 10 1 0 1 4

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Q: §3.7, Exercise 4. Let A, B,C be general n x n matrices. Simplify the expres- sion…

A: The given expression is A-1BA-1-1CB-1-1. Note that, if P, Q are invertible matrices, then we have…

Q: [3 Compute the natrix exponential e4t for the diagonal matrix A = !!

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Q: Show that the matrix A given below is singular. A = -2

A: A matrix is singular if it's determinant is zero.

Q: 2. Compute the following using the given matrix A. A= (a) A- (b) A + 2A +1

A: Inverse of matrix

Q: -1 -[::] Determine the dimensions of Nul A and Col A for the matrices. A = 4 7.

A: Before finding the column space or null space, we will reduce the given matrix to its reduced…

Q: 2. А %3D [0.7 0.1 Lo.1 0.7

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Q: In cach of the following, write the matrix A as a product SDS, where D is a diagonal matrix. ( ) 10…

A: We have to diagnose the above matrix.

Q: 2. find a matrix P that diagonalizes A, and compute p-AP. [500] Го о о A= 150 015 000 301

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Q: Find the elementary matrix E such that EB = A where 4 1 4 4 1 3 -1 -2 and B 18 -6 -12 %3D 5 -7 4 -7…

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Q: In Exercise, compute (a) ||A||2 and (b) cond2 (A)  for  the indicated matrix.

A: Given matrix is, A=10.911. We have to find the singular values of A. First find ATA as follows:…

Q: Prove the formula for a nonsingular n × n matrix A. Assume n ≥ 2.∣adj(A)∣ = ∣A∣n−1

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Q: a) Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

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Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix 2x -y = 5       x + 3y = -1

A: Given: The linear system of equations is, The inverse of a matrix is calculated by using the…

Q: Consider the matrix [1 2 3] B = |2 3 4 3 4 6 (a) Show, by calculating det B, that B has an inverse…

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Q: in number 1, B is the matrix representation of Z with respect to B only, not B and B'. The formula…

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Q: 2. Calculate the following matrix products: 1 -1 -1 3. A.

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Q: 1. Find a condition on a, b, c, d such that the augmented matrix " E b has a unique solution.

A: The condition on a,b,c,d must be a relation between a,b,c,d.

Q: 8. Prove that (i) ||7. =1, and (ii) |. =\n (I is the Identity Matrix of order n).

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Q: 2. Decompose the given matrix as indicated: [25 5 4] 10 8 16 8 12 22 1 Answer:

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Q: Find the elementary matrixE such that EB = A whe 4 4 1 4 4 1 3 -3 8 -6 A = -1 and B = 6 -6 -2 | 8 -6…

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Q: 5. Calculate the L and U matrix and proof that PA=LU. 10 -7 0 A = -3 26 5 -15

A: Firstly I find lower triangular matrix LL and an upper triangular matrix UU And the show that PA=…

Q: 7. The rank of an identity matrix of order n is: А. п - 1 В. п C. n+1 D. 0

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Q: 2. Verify, without using the matrix for 0(), that [O()]° is the identity matrix 1 0 0 1

A: This is a problem of rotation of the matrix.

Q: 1 4 What is a, if A = is a singular matrix ? %3D 2 a

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Q: Find a formula in terms of k for the entries of A, where A is the diagonalizable matrix below. 5-6 A…

A: Here we have to find a formula in terms of k for the entries of Ak, where A is the diagonizable…

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…

Q: [1 Find a matrix A = -4 -51 = l3. y] 1 z such that A² 10 %3D Lo 1. Lo

A: Given A=1xy01z001 A2-0-4-50010000=I3 To find Matrix A:

Q: 6) Find the SVD of the matrix by manually calculating U 4 11 14 A = 8 7 -2]

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Q: 2. Every square matrix A can be decomposed as a product of three matrices A = SDR where S and R are…

A: We shall give an counter example for part (2)

Q: 3. Consider the matrices A = |-1 2 2| and B= -1 1 1 -1 -1 (a) Find AT. (b) Compute A². (c) Calculate…

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Q: •(b) A = B:

A: Given,        A=-1201,   B=1-201

Q: Consider the matrix A = 0 o 0 0 -2

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Q: 5. Identify an elementary matrix E such that 1. E- 2 2 4.

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Q: Is it true or false? |A+ B" |=| A" + BT for any nxn matrices A and B. Birini seçin: O Doğru O Yanlış

A: To solve the above question we must know the following determinant property of any square matrix…

Q: Consider the following information regarding the number of men and women workers in three factories…

A: Represent in 3 x 2 Matrix form.

Q: Is it true or false? If A and B nxn matrices |A+B|=| A |+ | B| Birini seçin: O Doğru O Yanlış

A: we have to identify the following is true or false

Q: 1. A is a 22 matrix and det (A) - 4. what is det (3A)7 O 12 O 24 O 16 O 36

A: det(A)=4

Q: Find the elementary matrix E such that EC = A where %3D 4 4 A = |3 -1 and C = 3 0. -1 9 -8 19 0 4 ?…

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Q: Suppose A is a 5 by 5 matrix with det(A) = 6 What is det(AT A)? Answer:

A: Given det(A) = 6

Q: 4. Consider the following matrix A, where -2 4 -2 4 A = 2 -6 -3 1 -3 8 2 -3 Find bases for and…

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Q: 21 1 2 1 ol -1 A = | 0 2.

A: