Suppose A is a square matrix. Show (a) A+A" is symmetric, (b) A – A" is skew-symmetric, (c) A= B+ C, where B is symmetric and C is skew-symmetric.

Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

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Q: Give an example of a 3 x 3 skew-symmetric matrix A that is not diagonal. A =

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Q: What is the Skew-symmetric matrix?

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Q: If A = (aij) is the matrix of the quadratic form 7x + 5x, + 2x – 6x1x2 + 12x1x3 – 10x2x3, then the…

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Q: Show that a nonzero nilpotent matrix is defective.

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Q: Give an example of a matrix M where MMT and MTM are not equal matrices.

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Q: What is the transpose of matrix M=(-1,0,-2)(0,-3,1)?

A: Given -10-20-31

Q: Due to what property, applied to the matrices below, do we know that A + B = B + A?

A: Due to Commutative Property Of Addition of matrices, we can say that: A+B=B+A. Where, A,B,C are…

Q: If A and C arę nxn invertible matrices and B is an nxn matrix, then

A: By Theorem we can say that

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (a) (3,–4), (b) (1,2).

A: Result: Rows (columns) of an orthogonal matrix are an orthonormal basis. Hence, each row (column)…

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

A:

Q: Suppose AB = I, . Show that the equation Bx=0 has only trivial solution. Explain why the matrix not…

A: Suppose that AB=In (then x n  identity matrix). The objective is to show that, the equation Bx=0…

Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

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Q: Suppose A is a 5 x 5 nonsingular matrix, and Bis the result of exchanging the second and fourth rows…

A: If a matrix A is non-singular then all the rows and all the columns  of A are linearly independent.

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: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

Q: Suppose matrix A is m×n and B is n×p. If the first row of matrix A is all zeros, what can you say…

A: Explanation:Since matrix A is m×n and matrix B is n×p, the matrix AB will be m×p.In order to get the…

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

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Q: 6. If A is a 4 x 2 matrix and B is a 3 x 2 matrix, what is the size of ABT?

A:

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (а) (3, —4), (b) (1,2).

A: Find a 2x2 orthogonal matrix P whose first row is a multiple of(a) (3,-4) (b) (1,2)

Q: Due to what property, applied to the matrices below, do we know that A + B is a matrix of the same…

A: Given- Due to what property, applied to the matrices below, do we know that A + B is a matrix of the…

Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

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

A:

Q: Suppose A is a 3xn matrix whose columns span R3. Explain how to construct an nx3 matrix D such that…

A: Please check step 2 for the solution.

Q: Suppose that A is an 11 x 4 matrix, and that B is the rref of A. If the number of leading columns of…

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Q: Show that if a 3×3 matrix A is never sad then the entries along its diagonal, i.e. a11, a22, a33,…

A: Let 3×3 matrix A is never sad

Q: 32. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

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Q: Which matrix is not similar to

A: Given that Matrix- X= 011112-12114, A=21-121011114,B=01111411-122, C=0-111-12121-14, D=100030003,…

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

A: Consider Use the property of rank which states

Q: Suppose A is invertible and you exchange its first two rows to reach B. Is the new matrix B…

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Q: (4) Let A be a 3x3 matrix. If |4|= 2 , then |3.4|=,

A: Given that A be a 3*3 matrix and |A|=2. To find the value of |3A|

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

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

A:

Q: What is the linear combination of the matrices аnd

A: The explanation are as follows

Q: and B are square matrices with dimension 2 x 2, C is a matrix with 5 columns. What should be the…

A: Matrix CD is square matrix because A is square matrix.  And CD is define if column in C is equal to…

Q: If a square matrix has a row that is a multiple of another row, then it is singular. True or False

A: Answer is true

Q: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

A: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

Q: If A is 3 x 2 matrix and B is 2 x 3 matrix, then AB is always: a. Invertible matrix b. singular…

A: We know that rank ofAB is always less then or equal to min{rank(A), rank(B) }

Q: Suppose that A is a 16 x 14 matrix that has 6 pivot columns. Then: (i) dim (ColA) is (ii) dim(ColA)-…

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Q: Find a family of the matrices that is similar to the matrix -2] 寸 -3 4-

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: If A is a matrix in Rmxn with {()} -5 C(A) = span 2 %3D -2 what is m?

A: If A is a matrix in R^(m×n) then A is a linear transformation form n to m

Q: Suppose that A is a 7x8 matrix, and the dimension of the column space is 4. The dimension of the row…

A: A is 7×8(m×n,say) matrix . Given dimension of column space is 4.

Q: Find the nullspace of the matrix given as; A=[1 -2 1; 2 -3 5; 1 0 7]

A:

Q: Let A be a 5 × 4 matrix. Can the equation Ax=b be consistent for all b in ℝ5 ? Explain, please. Can…

A: Given that, A is a 5×4 matrix. Consider the equation, Ax=b. Here x is a 4×1 matrix with n=4 unknowns…

Q: If A is a 6×1 matrix and the sum A+B can be computed, what is the size of B?

A: Matrix addition. If A and B are matrices of the same size, then they can be added. (This is similar…

Q: Show that the matrix is not diagonalizable.

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

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