Is the matrix         1 0 0                               0 1 0                               0 0 1 inconsistent?

Q: Find the nullspace of the matrix

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Q: Show that the matrix is not diagonalizable.

A: Solve for det(A - λI) = 0

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

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Q: Determine the rank of the matrix. [10-4 0 4] 01-3 0 4 00 ΟΙΙ 0 0 0 0 0 05 02

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Q: Is this matrix invertible ? Explain 9 0 9 0 0 0 0 3 0 0 0 1

A: Introduction: For a square matrix A, if the existence of another square matrix B is confirmed so…

Q: Explain why the matrix A + C does not exist.

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Q: The matrix is not invertible for what value of x 2 1] 3 2 1 1 2

A: The matrix is not invertible the determinant of matrix should be zero.

Q: Find column rank, nullity, and the nullspace of the matrix 1 2 1 2 5 1 1 0. 3 7 2 2 -2 4 9 3-1 4

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Q: 3. Let A [1.1 -0.1] [0.3 0.7 0.7] Is matrix A invertible? How do you know?

A: An invertible matric is a matrix  for which matrix inversion operation exists . A matrix is said to…

Q: Find that whether the following matrix is singular or nonsingular. 8 0 -5,

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Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

A: Solution

Q: 0 4 13 4 0 -7 0 0 1

A: line of reflecton of a matrix is same

Q: 2 Discuss whether the matrix A 1 2 0 is diagonalizable or not. -3 5 2 ||

A: A matrix is said to diagonalizable if for every eigen value's algebraic multiplicity is equal to its…

Q: Determine the dimension of the nullspace of the matrix Г1 2 3 M 0 1 0 O 1 O 2 O 3

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Q: 2 0 -1 2 0 0 1 1

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Q: Show that any nX n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

A: To show that any n x n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

Q: Find an example of a singular 2 × 2 matrix satisfying A2 = A.

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Q: 4. Determine whether the matrix is nonsingular or singular. 6ive reasont -11 0 3 2-2 1 le

A: When the determinant of the matrix is zero,                      Then the matrix is said to be…

Q: Find the innverse of the matrix b: 5 0 6 9 1 2 3 4 9 3 5…

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Q: ГО 5 4 5 1 2 2 3] A = [1

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Q: Show that the matrix is not diagonalizable.

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Q: Could a rref matrix look like | 1 0 0 1 | | 0 1 0 1…

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Q: Find the nullspace of the matrix. 1 2 -2 1 A = |3 - 5 4 1 2 3.

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Q: Find the nullspace of the matrix.

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Q: Show that the matrix; is singular

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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: Find the singular value decompostion of the matrix. 1 1 -1 -1 1

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Q: Use the method of Example 6 to compute the matrix A10, where 1 0 6 2 A =

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Q: Given A = 1 1 0 3 Compute 5A *Matrix

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Q: Explain the rank of a n*n non-singular matrix?

A: Consider Use the property of rank which states

Q: Compute the indicated power of the matrix.

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Q: Is the matrix A invertible -1 2 3 -6 O True O False

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Q: Determine the size of the matrix. 1 -4 -1 0 5

A: Introduction :Given , we have asked to find the size of this matrix

Q: Find a fundamental matrix for the system = (; 3)* -2' x'(t) : 2 -2

A: x't=3-22-2x   Let A=3-22-2 Characteristic equation of A is given by  λ2-trAλ+detA=0 where trA is the…

Q: Can the null space of a 3 × 6 matrix have dimension 2? Explain.

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Q: Consider the matrix -1 1 -2 A = 3 2 2 1 1 -1 0 -2. 2 3 Compute det (A).

A: Given, A=0-100-2241301-1233-2 The value of the determinant is to be calculated.

Q: Find a 2 x 2 matrix such that 5 1 1 0 2 1

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Q: Find the nullspace of the matrix

A: We have given the matrix;

Q: find a 3 x 1 matrix x with entries no all zero such that Mx = 1x and            [ 1 2 -1 M =…

A: Consider a system of homogeneous equations. A system of equations can be solved by eliminating some…

Q: Find a matrix P that diagonalizes 1 0 0

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Q: 1. Show that matrix A is singular [1 2 0 A= 3 -1 2 -2 3 -2

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the nullspace of the matrix

A: The nullspace of the matrix is to be determined, The matrix is shown below as,

Q: Is the answer in #1 and #3 not in matrix form? how so?

A: Remember : eB represents coordinate matrix of e with respect to basis B. Which means if we consider…

Q: Give the rank and the nullity of the matrix. 20 -2 A = rank(A) = nullity(A) =

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Q: Determine the dimension of the matrix. 17 15 0 50 3 3 0 1 6 7

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Q: Find column rank, nullity, and the nullspace of the matrix 1 2 1 0 2 5 1 3 7 2 1 2 -2 4 9 3 -1 4 |

A: The nullity of a matrix A is the dimension of its null space: nullity(A) = dim(N(A)). It is easier…

Q: 3) For the matrix [2 1 -1 0 이 2 3 1 -1 4 3

A: The determinant of the matrix can be calculated by expanding along a row or by a column. The best…

Q: Find a 3x1 matrix X with entries not all zero such that AX = X , where [1 0 -1] A =1 0 1 4 -4

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Q: Show that the matrix is not diagonalizable.

A: Given matrix The characteristic polynomial of is the only Eigen- values are