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A is mxn matrix Problem 7 (10pts) Prove any TWO of the following: Let A be...
A is mxn matrix
Problem 7 (10pts) Prove any TWO of the following: Let A be a mx n matrix. Then • (AA+)+ = AA+ and (A+A)+ = A+A • A+ = (ATA)+AT = AT (AAT)+ • A+ = (ATA)-IAT and A+A = In if rank(A) = n, • A+ = AT (AAT)-1 and AA+ = Im if rank(A) = m, • A+ = AT, if the columns of A are orthogonal, that is ATA=In
4. Let A be a square matrix such that AAT-1. Show that AI = ±1. 4. Let A be a square matrix such that AAT-1. Show that AI = ±1.
4. Let A be a square matrix such that AAT-1. Show that AI = ±1.
4. Let A be a square matrix such that AAT-1. Show that AI = ±1.
A ternary matrix is a matrix whose entries are either 0,1 or 2. (a) How many...
A ternary matrix is a matrix whose entries are either 0,1 or 2. (a) How many ternary matrices of size mxn (that means, with m rows and n columns) are there? (b) How many ternary matrices of size 5x4 if 10 entries must be 0's, 6 entries must be 1's and 4 entries must must be 2's?
Let A = Construct a 4x2 matrix D
Let A = Construct a 4x2 matrix D, using only 1 and 0 as entries, such that AD = I2. Is it possible that CA =I4 for some 4X2 matrix C? Explain. Is it possible that CA = I4 for some 4 x 2 matrix C? Explain. Choose the correct answer below. A. No, because neither C nor A are invertible. When writing lm as the product of two matrices, since lm is invertible, those two matrices will also be invertible. B. Yes, because...
(a) Let A be a real n x m matrix. (i) State what conditions on n...
(a) Let A be a real n x m matrix. (i) State what conditions on n and m, if any, are needed such that the matrix AAT exists. Justify your statement. (ii) Assuming that the matrix AA exists, find its size. (iii) Assuming that the matrix AAT exists, prove using index notation that all diagonal elements of AAT are positive or equal to zero. (iv) Let 12 5 -3 A= 3-4 2 Calculate (AAT) -- (show all your working). 2)
Given a 2d matrix of size N x M (which must be read from a file...
Given a 2d matrix of size N x M (which must be read from a file provided to you), transpose it into a M x N matrix where N is the number of rows and M is the number of columns. void transpose(int n, int m, const int A[n][m], int AT[m][n]); Write a main() program to test and demonstrate your function. Show your function works for, at minimum, 3x6 and 10x6 matrices.
In this exercise, you will work with a QR factorization of an mxn matrix. We will proceed in the ...
In this exercise, you will work with a QR factorization of an mxn matrix. We will proceed in the way that is chosen by MATLAB, which is different from the textbook presentation. An mxn matrix A can be presented as a product of a unitary (or orthogonal) mxm matrix Q and an upper-triangular m × n matrix R, that is, A = Q * R . Theory: a square mxm matrix Q is called unitary (or orthogona) if -,or equivalently,...
In C++ Design a class to perform various matrix operations. A matrix is a set of...
In C++
Design a class to perform various matrix operations. A matrix is a set of numbers arranged in rows and columns. Therefore, every element of a matrix has a row position and a column position. If A is a matrix of five rows and six columns, we say that the matrix A is of the size 5 X 6 and sometimes denote it as Asxc. Clearly, a convenient place to store a matrix is in a two-dimensional array. Two...
Let A and E be matrices with the following sizes.A: 3 × 4 E: 4 × 3...
Let A and E be matrices with the following sizes.A: 3
× 4 E: 4 × 3
If defined, determine the size of the matrix E − 2A.
(If an answer is undefined, enter UNDEFINED.)
×
If not defined, explain why.
E − 2A is defined.
E − 2A is not defined because E and 2A have different
sizes.
E − 2A is not defined because E and 2A have the same size.
E − 2A is not defined because the...
JAVA PROGRAM. I need to write a program in java that will perform matrix addition and both matric...
JAVA PROGRAM. I need to write a program in java that will perform matrix addition and both matrices have N rows and M columns, N>1 and M>1. The two matrices must be divided to four equal size sub-matrices and each sub-matrix has dimensions N/2 X M/2. I need to create four threads and each thread performs a sub-set of addition on one pair of the sub-matrices. I also need an extra thread for networking. The network part of this uses...
A is mxn matrix
Problem 7 (10pts) Prove any TWO of the following: Let A be a mx n matrix. Then • (AA+)+ = AA+ and (A+A)+ = A+A • A+ = (ATA)+AT = AT (AAT)+ • A+ = (ATA)-IAT and A+A = In if rank(A) = n, • A+ = AT (AAT)-1 and AA+ = Im if rank(A) = m, • A+ = AT, if the columns of A are orthogonal, that is ATA=In
4. Let A be a square matrix such that AAT-1. Show that AI = ±1.
4. Let A be a square matrix such that AAT-1. Show that AI = ±1.
(a) Let A be a real n x m matrix. (i) State what conditions on n and m, if any, are needed such that the matrix AAT exists. Justify your statement. (ii) Assuming that the matrix AA exists, find its size. (iii) Assuming that the matrix AAT exists, prove using index notation that all diagonal elements of AAT are positive or equal to zero. (iv) Let 12 5 -3 A= 3-4 2 Calculate (AAT) -- (show all your working). 2)
In this exercise, you will work with a QR factorization of an mxn matrix. We will proceed in the way that is chosen by MATLAB, which is different from the textbook presentation. An mxn matrix A can be presented as a product of a unitary (or orthogonal) mxm matrix Q and an upper-triangular m × n matrix R, that is, A = Q * R . Theory: a square mxm matrix Q is called unitary (or orthogona) if -,or equivalently,...
In C++
Design a class to perform various matrix operations. A matrix is a set of numbers arranged in rows and columns. Therefore, every element of a matrix has a row position and a column position. If A is a matrix of five rows and six columns, we say that the matrix A is of the size 5 X 6 and sometimes denote it as Asxc. Clearly, a convenient place to store a matrix is in a two-dimensional array. Two...
Let A and E be matrices with the following sizes.A: 3
× 4 E: 4 × 3
If defined, determine the size of the matrix E − 2A.
(If an answer is undefined, enter UNDEFINED.)
×
If not defined, explain why.
E − 2A is defined.
E − 2A is not defined because E and 2A have different
sizes.
E − 2A is not defined because E and 2A have the same size.
E − 2A is not defined because the...
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