If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

Q: Can you provide one image or figure of the hermitian matrix?

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Q: Show that the matrix is not diagonalizable.

A: Solve for det(A - λI) = 0

Q: Show that the matrix is not diagonalizable.

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Q: Determine if the matrix is diagonalizable

A: Given matrix, A=200-121101 we know that, if a matrix A is an n×n matrix, then it must have n…

Q: must be a non-invertible matrix.

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Q: what is a Hermitian matrix? does every Hermitian matrix has to be square matrices?

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Q: Show that a nonzero nilpotent matrix is defective.

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Q: Determine whether the statement, 'Two 2 X 2 invertible matrices can have a matrix sum that is not…

A: Statement: "Two 2 X 2 invertible matrices can have a matrix sum that is not invertible" The above…

Q: If A is an invertible matrix, explain why A and AT must have the same null space. Is this true if A…

A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

Q: Prove that the main diagonal of a skew-symmetric matrix must consist entirely of zeros.

A: Given-Skew symmetric matrix. To prove- That the main diagonal of a skew-symmetric matrix must…

Q: Construct a 3 x 3 matrix, not in echelon form, whose columns do not span R. Show that the matrix you…

A: We have to construct a 3×3 matrix, which is not in the echelon form and whose columns do not span…

Q: Show that the matrix equation has no solution.

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Q: Is the matrix diagonalizable? If yes, find diagonal matrix D and regular matrix P such that AP = PD.…

A: Yes, Given Matrix is diagnolizable.

Q: Why is it important that the matrix is invertible? Give and example.

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Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

Q: Explain why the matrix is not diagonalizable.

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Q: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

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Q: Construct a 2 x 2 matrix that is diagonalizable but not invertible.

A: we have to construct a 2 x 2 matrix that is diagonalizable but not invertible.

Q: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

Q: Let A and B be two square Matrices of the same Size such that A is not invertible (B may or not be…

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Q: An n x n matrix that is orthogonally diagonalizable must be symmetric.

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Q: Show that the matrix is not diagonalizable.

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Q: The product of two invertible matrices is always non-zero. Select one: OTrue

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Q: • Is it possible for a 5 x 5 matrix to be invertible when its columns do not span R°? Why or why…

A: According to the Invertible matrix theorem, the matrix with n x n order cannot be invertible if its…

Q: Show that the matrix; is singular

A:

Q: Is there any 2x2 matrix with all non-zero entries, that is not diagonalizable but invertible? If…

A: Solution

Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: Due to what property, applied to the matrices and scalars below, do we know that c(A + B) = cA + cB…

A: Given: We have to state which property for c(A + B) = cA + cB and (c + d)A = cA + dA

Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: If A is an invertible square matrix that is row equivalent to matrix B , then both A and B are row…

A:

Q: Suppose A is anmxn matrix whose columns are linearly independent. What is the nullity of A?

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Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

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Q: Explain why the matrix is not diagonalizable.

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Q: find if the vector x is in the range for matrix A

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Q: Construct a 3 x 3 nonzero matrix A such that the vector is a solution of Ax = 0.

A: Given conditionAx = 0          .................(1)x = 111 is a solution to Ax=0,Let matrix A be - A…

Q: Determine if the matrix is diagonalizable.

A:

Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: Explain why the row vectors of a 4 × 3 matrix form a linearly dependent set. (Assume all matrix…

A: Given: The Matrix is 4 * 3 matrix

Q: Either the row vectors or the column vectors of a square matrix are linearly independent. True False

A: Any row vectors or column vectors of a square are said to be linearly independent if…

Q: For a square matrix A, AAT = ATA. %3D A) True False

A: We have to find the given statement is true or false.

Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

A:

Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…

Q: Determine whether the matrix B = is awesome or not. %3D

A: 7.1 To determine whether the matrix B is awesome or not. Where  B=i2−3232−i2and B is awesome if…

Q: Show that the matrix is not diagonalizable.

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

Q: Please show how to determine whether matrix A is diagonalizable: If possible, find an invertible P…

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Q: Let A be a matrix with more columns than rows.

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Q: A matrix which is not a square matrix is called a .6 Matrix

A: 6)  A matrix which is not a square matrix is called a

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.