9.1 (a) Write the following set of equations in matrix form: 40%3D 5х, + 2x, 10- x, = X3 4x, + 8x, 21 (b) Multiply the matrix of coefficients by its transpose; i.e., [A][A]°.

Q: 7. Given the following augmented matrix, list all the variables {x1, ... , X5}. Indicate which are…

A: We find free variables by using given augmented matrix.

Q: find the elelment in the 3rd row and 1st column of the matrix cofactor 7 2 5 3 1 4 1 2 1

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Q: For what values of r and s is the following matrix regular?

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Q: A is a 4 by 4 matrix with 1 's on the diagonal and -a, -b, -c on the diagonal above. Find A - 1 for…

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Q: 5. Find the rank and also the numerical rank of the matrix 1 1 .000a 0.000a where a is the last…

A: To find the rank and numerical of the matrix: 11.0007000.0007

Q: 1. Find the cofgctor of 6 in matrix B. 4 り り

A: We will find out the cofactor of 6 for given matrix B.

Q: 1. By hand, find the QR factorization of the matrix

A: QR factorization means A = QR Where, Q is an orthogonal matrix with orthogonal columns and R is an…

Q: Consider the following 3 x 3 matrix A and b in R, 1 -4 8 | A = 2 -3 2 1 5 -8 1

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Q: 1 What value of x satisfies the matrix equation -2

A: Number of Multiple questions as per our company guidelines we are supposed to answer only first…

Q: Compute the indicated power of the Matrix A = -3 5

A: We have to find the matrix A=-46-359.

Q: Which of the following is the order of its transpose in a matrix of the form ? * * O A) 6x2 О В) Зx3…

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Q: 2. А %3D [0.7 0.1 Lo.1 0.7

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Q: -2 Find the QR-factorization of the matrix A = 1

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Q: Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old),…

A: Here we have to use matrix multiplication to find number of birds of each category

Q: Determine the cofactor of a13 in the matrix. 2 -4 A =5 4 4 -4

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Q: What is the rank of the matrix?

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Q: Which of the following gives the correct matrix for this homogeneoussystem of equations in reduced…

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Q: Suppose A is a 5 x 5 matrix for which det(A) = -3. What is the value of det(2A)? det(2A) =

A: Sol:- Given :- Det(A) = -3 and Dimension of 5 * 5 Matrix

Q: 2 2 3. Transform the given matrix to RREF -2 1 1 -1

A: The given matrix is; 3 2 2 -2 0 1 1 -1 0. Repost the next question.

Q: 3. If A, B and C are matrices with orders, 3 X 3, 2 X 3 and 4 X 2, respectively, which of the…

A: Note: There are many subparts in the question. So I will answer the first three subparts.…

Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

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Q: 15. Let A be a 4 x 5 matrix and let U be the reduced row echelon form of A. If 21 -1)

A: a set B of vectors in a vector space V is called a basis if every element of V may be written in a…

Q: Q1 (d): Find the rank of the matrix A. 1 0 5 0 1 -2 2 -2 -1 1 -6 3 -2 12 2 -3 0 2

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Q: 1. АT 2. В — 2A

A: To find 1.A^T 2.B-2A

Q: What is trace of matrix (2A+3B)

A: Find the trace of the matrix(2A+3B)

Q: Diaganolize the following matrix. 0 0 -1 -1 0 0 3

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Q: Consider the matrix below A= 3 -2 4 0 -6 7 a 1 2 -2 1 -3 -4 3 1 2 Find the minor and cofactor of a

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Q: Compute the indicated power of the matrix.

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Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

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Q: of the following Is the fundamental solution matrix for the coefficient i ? 1

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Q: 2. Solve for x and y in the matrix equation below: x-y 4 2 [10 3 -1 4 3 -1] 1 2 4 x -8 2 6x -9 -3 3x…

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Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

Q: To divide the LHS by a matrix on the RHS, what steps do you follow?

A: To find: To divide the LHS by a matrix on the RHS, what steps do you follow?

Q: Find the rank of the following matrix. -1 3D1 0. 3. 4 2 1 4 |

A: given matrix is -1-100002340-213-104find the rank of the matrix

Q: What is the reduced row echelon form of matrix A? A = 어405 ON 11 O- O N

A:

Q: In a certain region, about 7% of a city's population moves to the surrounding suburbs each year, and…

A: Given: In a certain region, about 7% of a city's population moves to the surrounding suburbs each…

Q: An identity matrix is represented by... О а. Нн-1 O b. H-1H О с. Нн-1н

A: If we multiply a matrix by its inverse we get the identity matrix.

Q: Find the adjacency matrix for C_4 *

A: We need to find the adjacency matrix of the cycle C4.

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

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Q: .

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Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

Q: 1- the rank of the matrix A.

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Q: 1 Find the condition number of matrix -2 -3 4

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Q: Diaganolize the following matrix. 4 -1 0 1 6 -1 0 L0 0 0]

A: To diagonalize the given matrix.

Q: Find the LU- Factorization of the matrix A below 1 -2 3 A = 2 1 -4 4 1-4 6. 5 -2

A: Given 21-1-20321-441-465-2

Q: Suppose A is a matrix of order p × q and B is a matrix of order q × r, then illustrate the order of…

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Q: Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old),…

A: