Explain why the row vectors of a 9 x 6 matrix form a linearly dependent set. (Assume all matrix entries are distinct.) The rank of the matrix is at most So, the dimension of the row space is at most and any vectors in the row space must form a linearly dependent set.

Q: The reduced row echelon form of the matrix A is I3 . Describe all possible matrices A.

A: Consider the reduced row echelon form of a matrix A is I3. We need to determine all possible…

Q: Show that the matrix is not diagonalizable.

A: Solve for det(A - λI) = 0

Q: Suppose A is an m x n matrix whose columns are linearly independent. What is the nullity of A?

A: Given A is an m×n matrix whose columns are linearly independent. We have to find the nullity of A.

Q: Is the span of a matrix A is the same as the column space of A? T or F

A: We shall answer this question in next step

Q: Determine whether the matrix is orthogonally diagonalizable.

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

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Q: Determine whether the matrix is elementary. If it is, state the elementary row operation used to…

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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: Is it possible to find a matrix in row echelon form whose column (iv) space is the same as that of…

A: (iv) No , it is not possible to find a matrix in row echelon form whose column space is same as that…

Q: Give an example of a 3 x 3 lower triangular matrix A that is not diagonal. A =

A: We write the 3x3 lower triangular matrix which is not diagonal

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: Find three non-trivial 2 x 2 matrices such that the square of the matrix is the zero matrix, i.e: A?

A: We want to find matrix A such that A2 = 0000

Q: Let A be a 4x6 matrix. what is the dimension of Col A if the nullity is 2? Explain

A: 4

Q: Explain row vector in a 1 x n matrix?

A: To analyze row vector in a 1 × n matrix.

Q: Let A be a 3 x 5 matrix in which not all entries are zero. (a) What size must the matrix B be for AB…

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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: Determine by inspection whether the given set of vectors is linearly dependent or independent. Do…

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Q: Let A be an n × n matrix in which the entries of each row sum to zero. Find ∣A∣.

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Q: I, explain why BTB must be symmetric for any n × m matrix B. (If yo

A: We will prove that the matrix Is symmetric as following.

Q: Find a 2 x 2 matrix such that -3 1

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Q: Give an example of a 3 x 3 upper triangular matrix A that is not diagonal. A =

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Q: X1 – 2x2 + 3x3 ) 2х1 — Xә + 3хз 4x1 + x2 – x3 11 %3D 10 4

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Q: Explain why the row vectors of a 8 × 7 matrix form a linearly dependent set. (Assume all matrix…

A: Consider the given information. The given matrix in the form of 8 *7 matrix, forms a linearly…

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: In a matrix A, the dimension of the row space of A is equal to the dimension of the column space of…

A: The given statement is

Q: Explain why the row vectors of a 7 x 2 matrix form a linearly dependent set. (Assume all matrix…

A: Rank of the matrix is at most min(7,2) = 2 dimension of row space = rank of matrix

Q: Let A, B and C be 2x2 matrices that are invertible under matrix multiplication. Simplify (A CBC)as…

A: Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: ge multiplies to find the dimensions of a rectangular box with the largest volume if the total…

A: We have to find the dimension of given rectangular box.

Q: Find (a) a basis for the row space and (b) the rank of the matrix.

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Q: If A is an m × n matrix of rank r, what are the dimensions of N(A) and N(AT )? Explain.

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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: The row space of a matrix equals its column space. O True O False

A: Let the matrix Amxn having m rows and n columns. If the matrix has rank r after reduced Echelon…

Q: Let A be an m × n matrix. Explain why the matrix multiplications ATA and AAT are possible.

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Q: The row space and the column space of a matrix A do not have the same dimension. O True O False

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Q: Prove that the nonzero rows of a matrix in a row echelon form are linearly independent

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Q: 1 2 3 A = 1 3 2 2 6 8

A: See solution below

Q: Show that if the matrix X is diagonalizable, then X" is also diagonalizable.

A: Given that the matrix X is diagonalizable. We have to show that XT is also diagonalizable. Since,…

Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

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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: What is the rank of a 7x9 matrix whose null space is five dimensional? rank A =

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Q: Find a non-zero vector V in the row space of the matrix -20 4 0 -9 -3 12 -5 0 25 -12 -4 16 V

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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: ) If A is a 5 × 4 matrix, what is the largest possible dimension of the row space of A? If A is a 4…

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Q: Use part (iii) of the rank of a matrix by row reduction theorem to find the rank of the given…

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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

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.

A: