What is the difference between multiplying a matrix times a vector and multiplying two matrices?

Expert Solution

Colby Messinger answered 9 months ago

for matrices, what is the difference between row reduced echelon form and an upper triangular matrix?

4. The product y = Ax of an m × n matrix A times a vector...

4. The product y = Ax of an m × n matrix A times a vector x = (x1, x2, . . . , xn) T can be computed row-wise as y = [A(1,:)*x; A(2,:)*x; ... ;A(m,:)*x]; that is y(1) = A(1,:)*x y(2) = A(2,:)*x ... y(m) = A(m,:)*x Write a function M-file that takes as input a matrix A and a vector x, and as output gives the product y = Ax by row, as defined above (Hint: use...

Consider the problem of multiplying n rectangular matrices discussed in class. Assume, in contrast to what...

Consider the problem of multiplying n rectangular matrices discussed in class. Assume, in contrast to what we did in class, that we want to determine the maximum number of scalar multiplications that one might need (that is, compute the maximum of all possible parenthesizations). Formulate precisely an algorithm that determines this value. Then carry out your method on the following product to show what is the worst-possible parenthesization and how many scalar multiplications are required to carry it out: M9,1*M1,8*M8,2*M2,10*M10,4.

Consider the problem of multiplying n rectangular matrices discussed in class. Assume, in contrast to what...

Consider the problem of multiplying n rectangular matrices discussed in class. Assume, in contrast to what we did in class, that we want to determine the maximum number of scalar multiplications that one might need (that is, compute the maximum of all possible parenthesizations). Formulate precisely an algorithm that determines this value. Then carry out your method on the following product to show what is the worst-possible parenthesization and how many scalar multiplications are required to carry it out: M9,1*M1,9*M9,2*M2,8*M8,4.

4. The product y = Ax of an m n matrix A times a vector x...

4. The product y = Ax of an m n matrix A times a vector x = (x1; x2; : : : ; xn)T can be computed row-wise as y = [A(1,:)*x; A(2,:)*x; ... ;A(m,:)*x]; that is y(1) = A(1,:)*x y(2) = A(2,:)*x ... y(m) = A(m,:)*x Write a function M-file that takes as input a matrix A and a vector x, and as output gives the product y = Ax by row, as denoted above (Hint: use a for...

What is the difference between what is called the matrix and what is called the scaffold?...

What is the difference between what is called the matrix and what is called the scaffold? What is the nuclear matrix/scaffold and what does it consist of? What is a MARs and what are its general characteristics? What are some nuclear activities that are believed to be associated with the nuclear matrix?

Given the following two matrices: Matrix A that contains the marks of the college of engineering...

Given the following two matrices: Matrix A that contains the marks of the college of engineering students (250 Student) in 12 courses Matrix B that contains the number of credit hours of each course. Write a Matlab code to Print the letter grades (A to D) of student if you are given his ID and the course number from 1 to 12 Print his GPA in this semester. Gpa=sum(mark in subject i * subiect credit i) /total number of credit,...

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What is the difference between multiplying a matrix times a vector and multiplying two matrices?

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