Let A be an nn nonsingular lower triangular matrix; that is,
a11a21a31an10a22a32an200a33an3000ann where aii=0 for 1in. Let b=[b1,b2,,bn]T denote a
(column) vector with n entries. A system of linear equations Ax=b can be solved by "forward"
substitution, which is very similar to back-substitution but starts with the first equation. (a) (2
points) Fill in the blanks in the following algorithm (use pseudocode, not MATLAB) so that it
will solve such a system of linear equations. x1fori=sumforj= end for end for (b) (2 points) Give
a floating-point operation (flop) count for this forward substitution algorithm. That is, determine
the total number of floating-point additions, subtractions, multiplications and divisions (as a
function of n ) that this algorithm will execute.
(c) (2 points) Convert your pseudocode to MATLAB or Python code and write a function that
takes as input the nonsingular lower triangular matrix A, and column vector b and returns the
results of "forward" substitution. The input matrix should be the full matrix including the zeros.
Show how your function can be called and what the result is for the following matrices A and b :
A=12470358006900010,b=151534.
Let A be an n�n nonsingular lower triangular matrix; that is, a11a21a.pdf
1. Let A be an nn nonsingular lower triangular matrix; that is,
a11a21a31an10a22a32an200a33an3000ann where aii=0 for 1in. Let b=[b1,b2,,bn]T denote a
(column) vector with n entries. A system of linear equations Ax=b can be solved by "forward"
substitution, which is very similar to back-substitution but starts with the first equation. (a) (2
points) Fill in the blanks in the following algorithm (use pseudocode, not MATLAB) so that it
will solve such a system of linear equations. x1fori=sumforj= end for end for (b) (2 points) Give
a floating-point operation (flop) count for this forward substitution algorithm. That is, determine
the total number of floating-point additions, subtractions, multiplications and divisions (as a
function of n ) that this algorithm will execute.
(c) (2 points) Convert your pseudocode to MATLAB or Python code and write a function that
takes as input the nonsingular lower triangular matrix A, and column vector b and returns the
results of "forward" substitution. The input matrix should be the full matrix including the zeros.
Show how your function can be called and what the result is for the following matrices A and b :
A=12470358006900010,b=151534
![Let A be an nn nonsingular lower triangular matrix; that is,
a11a21a31an10a22a32an200a33an3000ann where aii=0 for 1in. Let b=[b1,b2,,bn]T denote a
(column) vector with n entries. A system of linear equations Ax=b can be solved by "forward"
substitution, which is very similar to back-substitution but starts with the first equation. (a) (2
points) Fill in the blanks in the following algorithm (use pseudocode, not MATLAB) so that it
will solve such a system of linear equations. x1fori=sumforj= end for end for (b) (2 points) Give
a floating-point operation (flop) count for this forward substitution algorithm. That is, determine
the total number of floating-point additions, subtractions, multiplications and divisions (as a
function of n ) that this algorithm will execute.
(c) (2 points) Convert your pseudocode to MATLAB or Python code and write a function that
takes as input the nonsingular lower triangular matrix A, and column vector b and returns the
results of "forward" substitution. The input matrix should be the full matrix including the zeros.
Show how your function can be called and what the result is for the following matrices A and b :
A=12470358006900010,b=151534](https://image.slidesharecdn.com/letabeannnnonsingularlowertriangularmatrixthatisa11a21a-230329124242-8d9d33c3/85/Let-A-be-an-n-n-nonsingular-lower-triangular-matrix-that-is-a11a21a-pdf-1-320.jpg)
