Show that if A is any m × n matrix, then Im A = A and AIn = A.

Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

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Q: Determine whether the statement below is true or false. Justify the answer. If A is an mxn matrix…

A: I assume you know what is an argument matrix and what is rank of matrix .

Q: Determine whether the given matrix is diagonalizable 3 1 A = 0 1 3

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Q: Let A be an m × n matrix. Show that A is row equivalent to O if and only if A = O .

A: Consider the given information as A be an n×nmatrix

Q: Let A be square matrix. If A" = 0. A= Oava %3D for n> 2. Then

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Q: Let A be a 5x7 matrix, then the smallest possible dimension of Null(A) is:

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Q: If P is an n x n matrix with orthogonal columns, then PT = P-1 Select one: True False

A: Let P be the given orthogonal matrix

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

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Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: If the RREF of All is || B, then AB is the identity matrix. A) True B False

A: Given: The row reduces echelon form is A:I is I:B. We have to check whether AB is the identity…

Q: Suppose that A is an m x n matrix and B is an n x m matrix. Then the equation (AB) = ATBT is always…

A: Multiplication Property of transpose : We know that the transpose of a produce of two matrices will…

Q: If A is a real n xn matrix, show that AA" and ATA are similar. (Hint. Start with an SVD for A.)

A:

Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

Q: If A is a square matrix, then Ker(A) = Ker(RREF). True or false?

A: If A is aquare matrix then we have to check Ker(A) =Ker(RREF(A))

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

A:

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: If A is an orthogonal matrix, find a QR factorization of A

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Q: Suppose that A+ is a 2 × 2 matrix and that A+ = -A. Show 7.2 that iA is awesome.

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Q: Let A be an m x n matrix with m>n.  Show that for any n x m matrix B, then AB does not equal Im. Use…

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Q: Find diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

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Q: If A is a square matrix such that some row of A2 is a linear combination of the other rows of A2,…

A:

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

A: Sum of symmetric and skew-symmetric matrix is matrix it self. Like for matrix A, Symmetric matrix =…

Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

A: GivenA=3121

Q: If A is a m × n matrix and B is a n × p matrix then AB is a m × p matrix. True or False

A:

Q: Let A be an nxn matrix and B = A+1, where I is the identity matrix, then it is possible for A and B…

A: Given A be an n×n matrix nd B=A+I where I is the identity matrix , then it is possible for A and B…

Q: If A is square matrix of order 3 such that|3 A| = 54. Find |A|

A: Using the properties of determinants

Q: Let A be a square matrix and det(A) = 2. If B is the matrix that results when –7 times the - first…

A: Given that: det(A)=2

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

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

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Q: Show that if A and B are n × n matrices and N(A − B) = Rn then A = B.

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Q: If A is an n Xn matrix then det(A)=Ddet(-A). Select one: True False

A: Given Statement If A is an nxn matrix then det(A)=det(-A).

Q: 2. Let A be a 7 x 5 matrix, and suppose AB is a 7 x 9 matrix for some matrix B. What must the size…

A: We know that matrix multiplication is possible only when number of column of first matrix is equal…

Q: If A is a square matrix, then A2 is defined. TRUE OR FALSE

A: For matrix multiplication to be defined, the number of columns in the first matrix must be equal to…

Q: Let A be an n xn matrix and B= A+I, where I is the identity matrix, then it is possible for A and B…

A:

Q: Suppose a 6 x 8 matrix A has four pivot columns. What is the dim (Null A)? Is Col A = Rª ? Explain.

A: see below the answer

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

A:

Q: Let A be an n × n matrix and c a real number. Show that if cA = O , then c = 0 or A = O .

A: Given: A be an n × n matrix and c be a real number. To prove that: if cA=0 , then c=0 or A=0.

Q: If A is what a matrix satis fying A3= A about det A7 %3D can you say

A: We have to find determinants

Q: Let A be an nxn matrix and B= A+I, where / is the identity matrix, then it is possible for A and B…

A:

Q: Show that if a square matrix A has two equal columns, then A is not invertible.

A: since not a particular question asked ,as per guidelines solution to only first question (i.e Q1) is…

Q: Let A be an n × n matrix and let B = A + AT and C = A − AT (a) Show that B is symmetric and C is…

A: given: let A be a n×n matrix. B=A+AT C=A-AT we have to show that B is symmetric matrix and C is skew…

Q: Let A be a 3x3 matrix where A2=I3, then det(A) is 1 or -1. Select one: 1-True 2-False

A: To find- Let A be a 3×3 matrix where A2 = I3, then detA is 1 or -1. True False

Q: Suppose A and I are bothn x n matrices, then

A:

Q: If Ā is a 5 × 5 skew symmetric matrix, show that det Ā = 0.

A: A n×n order matrix A= is said to be skew symmetric matrix if the following condition hold…

Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

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Q: ) If A is a square matrix such that some row of A² is a linear combination of the other rows of A²,…

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Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.