s3w7 gaussian elimination and Cramers rule.

Questions 1 & 2

03:14

Question 3

07:33

1

Some versions of gaussian elimination require you to reduce the right side of the system to the identity matrix rather than the row echelon form. What is the difference between this version and the one the lady above explained?

Question 5

01:38

Questions 6 & 7

03:45

1

Watch the following video explain inverse matrices. pay attention to the inverse matrix part. you don't need to worry too much about rank, column space and nullspace. do pay attention about what it means for the inverse if the determinant is 0. do you have any questions?

1

how do you take the inverse of a 3x3 matrix

create a matrix of minors, reflect the values across the diagonal

create your matrix and an equal sized identity matrix side by side. perform gaussian elimination on the matrix until you get it to an identity matrix. each time you perform any action, perform the same action on the identity matrix. When you have gotten the matrix into identity form, your identity matrix will now be the inverse matrix.

reflect the values across the diagonal, take the determinant and apply the plus/minus grid

use desmos matrix calculator.

1

notice one of the things about matrices is that A \cdot B \ne B \cdot A when we have A \cdot \vec{x}=\vec{v} and we multiply both sides by A^{-1} we have to multiply both sides _on the same side_. we call this right and left multiplication. what would it mean if you multiplied A^{-1} on the right on one side of the equation, and on the left on the opposite side?

1

There is a whole 3blue1brown video explaining Cramer's rule geometrically. You can dig into that if you want, it decided that one was probably a bridge too far. you are welcomed to watch it if you want. For Cramer's rule:
which of the following describes D_x?

It is the coefficient matrix with the first row replaced with the solution matrix

It is the coefficient matrix with the first column replaced with the solution matrix

It is the vector <x,y,z> left-multiplied by the coefficient matrix

it is the vector <x,y,z> right-multiplied by the coefficient matrix

1

How did the 3blue1brown videos explain why A\cdot B \ne B\cdot A?

matrix multiplication is more like division. a\cdot b=b\cdot a, but \frac{a}{b} \ne \frac{b}{a}

matrix multiplication is more like a function applied to another function. f(g(x)) \ne g(f(x))

matrix multiplication is more like addition. A+B \ne B+A

those are equal.

1

For a linear transformation to be considered linear, the transformation needed

grid lines to remain straight and equally spaced

grid lines to remain straight

grid lines to remain equally spaced

none of these apply

1

I'd mentioned that we are ripping through matrices at a decent clip. so I will set the scene for the next week - what are some tell tale signs a set of simultaneous equations are not linear.

1

how would you deal with simultaneous inequalities differently than you would simultaneous equalities?

1

categorize your understanding

algorithm for gaussian elimination
when to use gaussian elimination
what is cramers rule
how do you find the A_x, A_y, A_z matrices you need for cramers rule
how to find the determinencts of those matrices for cramers rule
When to use cramers rule
how are linear transformations related to matrices?
how do you break apart fractions

Ive got this
im fuzzy
so confused

s3w7 gaussian elimination and Cramers rule.

The form of a matrix that has all 0s on the bottom side of the diagonal is called "Row Echelon Form". Why do you think row echelon form might be useful?

notice that you are allowed to swap rows if that makes your life easier. just make sure you swap the entire row.

Some versions of gaussian elimination require you to reduce the right side of the system to the identity matrix rather than the row echelon form. What is the difference between this version and the one the lady above explained?

Note that finding the determinant for a 3 or 4 square matrix is also time consuming and fraught with mistakes, but this is what matrix calculators are for. no question - just wanted to highlight that.

Also note what will happen if the determinant of the original matrix is 0. What do you think you can say when the determinant is 0?

Watch the following video explain inverse matrices. pay attention to the inverse matrix part. you don't need to worry too much about rank, column space and nullspace. do pay attention about what it means for the inverse if the determinant is 0. do you have any questions?

how do you take the inverse of a 3x3 matrix

There is a whole 3blue1brown video explaining Cramer's rule geometrically. You can dig into that if you want, it decided that one was probably a bridge too far. you are welcomed to watch it if you want. For Cramer's rule:
which of the following describes D_x?

How did the 3blue1brown videos explain why A\cdot B \ne B\cdot A?

For a linear transformation to be considered linear, the transformation needed

I'd mentioned that we are ripping through matrices at a decent clip. so I will set the scene for the next week - what are some tell tale signs a set of simultaneous equations are not linear.

how would you deal with simultaneous inequalities differently than you would simultaneous equalities?

categorize your understanding

The form of a matrix that has all 0s on the bottom side of the diagonal is called "Row Echelon Form". Why do you think row echelon form might be useful?

other videos will want you to get your matrix to "reduced row echelon form" to make everything simple. What do you think reduced row echelon form is?

notice that you are allowed to swap rows if that makes your life easier. just make sure you swap the entire row.

Some versions of gaussian elimination require you to reduce the right side of the system to the identity matrix rather than the row echelon form. What is the difference between this version and the one the lady above explained?

To find D_x you have to

Note that finding the determinant for a 3 or 4 square matrix is also time consuming and fraught with mistakes, but this is what matrix calculators are for. no question - just wanted to highlight that.

Also note what will happen if the determinant of the original matrix is 0. What do you think you can say when the determinant is 0?

Watch the following video explain inverse matrices. pay attention to the inverse matrix part. you don't need to worry too much about rank, column space and nullspace. do pay attention about what it means for the inverse if the determinant is 0. do you have any questions?

how do you take the inverse of a 3x3 matrix

There is a whole 3blue1brown video explaining Cramer's rule geometrically. You can dig into that if you want, it decided that one was probably a bridge too far. you are welcomed to watch it if you want. For Cramer's rule:
which of the following describes D_x?

How did the 3blue1brown videos explain why A\cdot B \ne B\cdot A?

For a linear transformation to be considered linear, the transformation needed

I'd mentioned that we are ripping through matrices at a decent clip. so I will set the scene for the next week - what are some tell tale signs a set of simultaneous equations are not linear.

how would you deal with simultaneous inequalities differently than you would simultaneous equalities?

categorize your understanding

other videos will want you to get your matrix to "reduced row echelon form" to make everything simple. What do you think reduced row echelon form is?

To find D_x you have to

s3w7 gaussian elimination and Cramers rule.

s3w7 gaussian elimination and Cramers rule.

Some versions of gaussian elimination require you to reduce the right side of the system to the identity matrix rather than the row echelon form. What is the difference between this version and the one the lady above explained?

Watch the following video explain inverse matrices. pay attention to the inverse matrix part. you don't need to worry too much about rank, column space and nullspace. do pay attention about what it means for the inverse if the determinant is 0. do you have any questions?

how do you take the inverse of a 3x3 matrix

There is a whole 3blue1brown video explaining Cramer's rule geometrically. You can dig into that if you want, it decided that one was probably a bridge too far. you are welcomed to watch it if you want. For Cramer's rule: which of the following describes D_x?

How did the 3blue1brown videos explain why A\cdot B \ne B\cdot A?

For a linear transformation to be considered linear, the transformation needed

I'd mentioned that we are ripping through matrices at a decent clip. so I will set the scene for the next week - what are some tell tale signs a set of simultaneous equations are not linear.

how would you deal with simultaneous inequalities differently than you would simultaneous equalities?

categorize your understanding

Some versions of gaussian elimination require you to reduce the right side of the system to the identity matrix rather than the row echelon form. What is the difference between this version and the one the lady above explained?

Watch the following video explain inverse matrices. pay attention to the inverse matrix part. you don't need to worry too much about rank, column space and nullspace. do pay attention about what it means for the inverse if the determinant is 0. do you have any questions?

how do you take the inverse of a 3x3 matrix

There is a whole 3blue1brown video explaining Cramer's rule geometrically. You can dig into that if you want, it decided that one was probably a bridge too far. you are welcomed to watch it if you want. For Cramer's rule: which of the following describes D_x?

How did the 3blue1brown videos explain why A\cdot B \ne B\cdot A?

For a linear transformation to be considered linear, the transformation needed

I'd mentioned that we are ripping through matrices at a decent clip. so I will set the scene for the next week - what are some tell tale signs a set of simultaneous equations are not linear.

how would you deal with simultaneous inequalities differently than you would simultaneous equalities?

categorize your understanding

other videos will want you to get your matrix to "reduced row echelon form" to make everything simple. What do you think reduced row echelon form is?

To find D_x you have to

There is a whole 3blue1brown video explaining Cramer's rule geometrically. You can dig into that if you want, it decided that one was probably a bridge too far. you are welcomed to watch it if you want. For Cramer's rule:
which of the following describes D_x?

There is a whole 3blue1brown video explaining Cramer's rule geometrically. You can dig into that if you want, it decided that one was probably a bridge too far. you are welcomed to watch it if you want. For Cramer's rule:
which of the following describes D_x?