24 --8 Find the rank of the matrix A =0 1 -2 4 8 -18 rank(A) =

Q: 5 -1 Find the transpose of the matrix: -21 27. 33

A:

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

A:

Q: 2 1 -1 3 1 2 1 2 0 b) Calculate the rank of the matrix P = 3 1 1 1 |-1 -5 -3 -7 3

A: Given,

Q: 6 1 is similar to the matrix B = 3 4 7 0 The matrix A = Select one: True False

A:

Q: -1 10 2 4 5 2 10 coeFFICient of matrix (A) 2 3 -5 2

A:

Q: -2 1 -1 -3 1 3 b) Find the Rank and Nullity of a matrix A = -2 -1 1 -1 3 3 9 0 -12

A: Concept:

Q: 3. Diagonalize the matrix A = 1 -3 3 3 3 -5 -3 3 1 if possible.

A:

Q: 1 2 3 1 A = 1 0 1 -1 2 1 1 Find rank of the matrix

A: We have to find the rank of the given matrix…

Q: -1 2 3 - 5 2 , Find the rank of the matrix 3 - 8 5 5 -12

A: The matrix is given as -123-22-5123-8525-12-16 Convert this matrix to echelon form Consider…

Q: 1 2 3 -27 2 -5 1 If A then the = 3 -8 -12 -1 rank of the matrix A is

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Q: -1 2 4 Find the 1-norm of the matrix 3 -2 0 1 -1 2.

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Q: h-2 -4 -2 3 -6+3h -9 -5 8 Decompose the matrix A= -3 -1 6 into L and U matrices by using the method…

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Q: 32 40 72 Given the rank one matrix A = -20 -25 –45 -45 -24 -30 -54 -54 what is x?

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Q: [1 -3 Determine the matrix -31 if it is a linear combination of a b

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Q: -2 5 Find the characteristic equation of the matrix 3 5 C. 22 – 32 – 25 = 0|| D. 2? +72 - 25 = 0 A.…

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Q: 2 1 0 -1 3 1 Calculate the rank of the matrix P = 1 2 0 3 1 1 1 -1 - 5 -7 3 -

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Q: Let the matrix A be given by -11 1. -5 0 2. -1 3

A: Given matrix is 10-11 21-50 1-100 0003 To find:  Minor M11 Cofactor C11

Q: 8. 3 a) Let A = ( 6 1 3 ,B = 6 -2/ %3D 1 Then find the matrix AB. -4 -1

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Q: 1 -2 0 4 3 Calculate the rank of the matrix P = 1 1 -1 -5 -1 3 8 2 -12

A: The matrix P is,P=1-2043110-1-5-18382-12To find its rank.

Q: What is the rank of the matrix?

A:

Q: 4 8 -12 A--16 -32 49 20 40 -55 Express A in the form A LDU, where L, is lower triangular with 1's…

A: Lower triangular matrix: A square matrix in which all the elements above principal diagonal are zero…

Q: 1 -2 Diagonalize the matrix B 3 -4 ||

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Q: (-1 7 -5 7. Let A = -4 11 -6). Diagonalize A if possible or explain why the matrix A is not -4 8 -3.…

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Q: 3] [1 2 Find A¹ of The Matrix A = 3 2 -1 3 1 2]

A: As per the instruction, we will be answering the first one. Given: Now,…

Q: 1. Find an LU factorization of the matrix A 5 [2 A = [4 L4 3 9. -3 24]

A: In Linear algebra, lower–upper decomposition or factorization factors a matrix as the product of a…

Q: 1 3 1 -1 0 1 Consider the matrix A = -3 2 1 -2 1 4 1 6 1 3

A: Let us apply elementary row operations on the augmented Matrix [A|b] to reduce it in row reduced…

Q: 3 -4 Find the dimension of the matrix 2 4 -2 -5]

A: In the matrix Total number of  rows = 3 Total number of columns = 2

Q: 6: [1 The rank of the matrix A = 4 15 True O False 2 2 5 7 31 6 is equal to 3. 9

A:

Q: -3 4 0 3 2 1 -1 3 о 1 -1 0 0 0 5 0 0 0 0 4 der the matrix A = 1 3 8. 1.

A: In this question, the following conditions are checked. Lower triangular matrix. Diagonalizable.…

Q: 1 0.1 0.9 3 -12 6 Given Matrix A = 4. 1 -5 5 1. 17 6 -2

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Q: 9. 7 Find the rank of the matrix A = 1 -2 %3D 27 21 13 rank(A) = %3D

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Q: 1.) Determine [-5 aces the dimension of the matrix. -9 7 28 13 3 X 10 -1 7 1 ka-

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Q: 1 3 -5 -3 Find the LU factorization of the matrix: A =-1-5 8 4 4 2 -5 -7

A: We use the Gaussian Elimination Method to find the LU factorization of the given matrix A.

Q: 4.) Determine matrix. 2-3 1 2 -2 6 X the dimension of the

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Q: a) (11-1) If A = 0 -2 3 001 , Show that A² = −4+27, where is the identity matrix.

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Q: 4 -3 2 Given the matrix A = 5 -2 0 \1/2 3 7 -5/2/ (a) Calculate az31 + a13 and az4 + a24 (b)…

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Q: [1 -2 -1] with |4|=-7. Let A= 0 1 |3 -1 0 Matrix B is obtained by modifying matrix A, with B+ A.…

A: The detailed solution is as follows below:

Q: 3. (30 points) Diagonalize the matrix A = 5 0 1 -1 05 0 0 0 0 4-3 0 -2 0-3 if possible.

A: 5000050000-30000-3

Q: 4] -9 0 -8 1 1 -2 -2 13 Consider the matrix -4 3 -1 2 1

A: let B=1-2-21342-43-90-121-81 claim- to find the right inverse of the matrix

Q: 6: [1 The rank of the matrix A = 4 [5 O True False 2 3 5 7 6 is equal to 3. 9]

A:

Q: -4 1 -1 The rank of the matrix -1 -1 -1 7 -3 1

A: Given matrix is A = -41-1-1-1-17-31

Q: 3. Determine the rank and nullity of the matrix -1 1 2 -1 1 A = (-1 -1 4 1 -3 -3.

A: Consider the following matrix: A=2-11-1-1-12141-3-3 Convert matrix A to row echelon form:…

Q: 1 3 4 Find the rank of the matrix A 2 8 10 5 15 - 20 rank(A) Check Answer

A: To find The rank of the given matrix.

Q: Diagonalise the symmetric matrix A = 4 2 2 2 4 2 2 2 4

A: Given symmetric matrix is  We have to diagonalise the above matrix. First we will find the…

Q: 1 0 0 - 4 - 2 07 - 4 0 -4 1 Find the size of the matrix 4 -1 0 2 1 5 1 4 5 3 - - 2 1 4 - 4 1

A: The objective is to find the size of the matrix.

Q: 2. Orthogonally diagonalize the matrices. -4 4 1 5 (a) 5 1 (b) |-4 4 9

A: The given matrices are; a)  1 5       5 1 b).   7  -4  4        -4  5  0         4  0  9

Q: 5 15. Let A be the matrix -3 1 (a) Compute A-!. (b) Use part (a) to find the unique solution to the…

A:

Q: 2 5 -7 (b) Express-9 12 4 as the sum of a lower triangular matrix and an upper trian- 15 -13 6.…

A: Solved below