Describe the possible echelon forms of the following matrix. A is a 6x3 matrix, A = a, az az , such that {a,, a2} is linearly independent and az is not in Span{a,, a2}.

Q: All the diagonal elements of a skew-symmetric matrix is: * 1 2 Any Integer

A:

Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 0, a2 = 2, a33 = 5, a21 = 3, a31 = 4, and…

A: a symmetric matrix is a square matrix that is equal to its transpose.

Q: Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is called…

A: Here we have to determine whether the matrix is symmetric, skew-symmetric or neither.

Q: Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly…

A:

Q: Let w = ( -1, -4, -9). By appropriate use of the augmented matrix and elementary row operations…

A: We have to check that w is linear combination of given vectors or not.

Q: Determine whether the matrix is in echelon form, reduced echelon form, or neither. 1 4 5 -7 4 1 -4 7…

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Q: (d) Let C be an nXn matrix. Explain why if the echelon form of C has at least one zero row, then C…

A: To prove, if matrix C has at least one zero row then the matrix is not invertible.

Q: Let A be an m×n matrix with rank m and B be an n×p matrix with rank n. Determine the rank of AB.…

A: This can be done as follows:

Q: Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear…

A: We have to find the value of h such that the matrix is the augmented matrix of a consistent linear…

Q: Determine whether the matrix is in echelon form, reduced echelon form, or neither. [1 0 0 -7* 1 10 1…

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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: Find the echelon form of this augmented matrix, written so there are 1's on the diagonal. 1 -2 100…

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Q: Determine whether the matrix is symmetric, orthogonal, both, or neither.

A: To determine whether the matrix is symmetric, orthogonal, both, or neither.

Q: For any square matrix A, AAT is a a. Diagonal matrix b. Symmetric matrix O c. Skew symmetric matrix…

A: For any square matrix A to find AAT  is which f the following.

Q: Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in…

A: We have to solve the problem

Q: Do the columns of the matrix span IR? Select an Answer v 1. 3 3 -3 3 A = -5 -4 3 -1 -4 -4 4 -4…

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Q: Matrix A: 1 3 4 6.

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Q: A C 6 2 C 2 -1 c

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Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5«5)) = %3D

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Q: Consider the matrix 1 1 a A := 1 b b C C Find all possible combinations of values a, b, c E R for…

A: We have to find possible value of a,b and c for which matrix is invertible.

Q: Describe the possible echelon forms of the following matrix. Ais a 3x3 matrix with linearly…

A: Given: To describe the possible echelon form of the following matrix. A is a 3x3 matrix with…

Q: If A is a square matrix whose diagonal entries are all zero, then detA = 0.

A: Given information: A is a square matrix whose diagonal entries are all zero.

Q: Find an LU-factorization of the matrix: show solutions. 1 1 a. 1 ⠀⠀ 2 2 2 3 2 5 b. 6 14

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Q: If A is a skew symmetric matrix, what type of matrix is A T ? Justify your answer.

A: Given: A is a skew-symmetric matrix.

Q: Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.…

A: let the given matrix is an augmented matrix of a consistent linear system and that is: A=5-7h-20284

Q: Let A be a 3 x 3 matrix with columns a1, a2, a3. Suppose that A has the following properties: • aj…

A: Columns a1 and a2 are linearly independent and the third column can be written in terms of a1 and…

Q: Suppose A is an x n matrix. (a) If ker(A) = (b) Give an example of a matrix with ker(A) = im(A).…

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Q: b. If possible, produce a diagonal matrix similar to the following one 2 2 1

A: Use the following formulae, to obtain the solution. The eigenvalues λ1 and λ2 of the matrix A are…

Q: Determine if the matrix is symmetric. -1 9 0 6. 0 9 The transpose of the given matrix is Because…

A: Let A be the given matrix A = 0-19-106960 We have to determine the given matrix is symmetric or not…

Q: a) Let A be a 3 x 5 matrix

A: For the multiplication of two matrix the number of columns in first matrix is equal to the number of…

Q: Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear…

A:

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: 7 |-4 [3 а 4

A: Augmented matrix173a-44170a-21-416apper triangular formx+7y=-40.x+y(a-21)=16Equivalent system

Q: Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is…

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Q: If A is 3x3 nonsingular matrix such that AA =A A and B=A A then BB= -1 T Select one: -1 a. В -1.T b.…

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Q: Jse a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: Let A be a 4 × 5 matrix. If a1, a2, and a4 are linearly independent and a3 = a1 + 2a2, a5 = 2a1 − a2…

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Q: Describe the possible echelon forms of the matrices below using 0, 1 for the pivot and * for all…

A: See the detailed solution below.

Q: A square matrix A is called joyous if it is symmetric, all its diag

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Q: 9. A = -2 2

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Q: b) Diagonalize the following matrix, if possible 2 2 -1] 3 -1 -1 -2 1 2

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Q: V. Let A be a 3×3 matrix and let b= 3a, +a, +4a,· Will the system Ax=b be consistent? Explain.

A: Given that A is a 3*3 matrix andet b=3a1+a2+4a3

Q: e reduced row echelon form of the matrix B.

A: In this question, the concept of row reduced echelon form is applied. Reduced Row Echelon Form When…

Q: Use the reduce echelon form "triangle upper matrix" to find the det(A), where A = 2 -8 6 8 3 -9 5 10…

A:

Q: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: 3. let A be a 3x3 matrix and Auppose that A + 2a,- 30z=0, where a,, a,and az are the Colums of the…

A: System of Linear equations and non singularity

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: Determine whether the matrix A is in Reduced Row Echelon Form: 0 1 0 0 0 1 0 00 A = True False

A: Correct ans is - True

Q: Determine the value of hh such that the matrix below is the augmented matrix of a consistent linear…

A: Given the matrix is 8-4-168h9

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.