Given a system of equations, solve with matrix inverses using a calculator.
Save the coefficient matrix and the constant matrix as matrix variables
and
Enter the multiplication into the calculator, calling up each matrix variable as needed.
If the coefficient matrix is invertible, the calculator will present the solution matrix; if the coefficient matrix is not invertible, the calculator will present an error message.
Using a calculator to solve a system of equations with matrix inverses
Solve the system of equations with matrix inverses using a calculator
On the matrix page of the calculator, enter the
coefficient matrix as the matrix variable
and enter the constant matrix as the matrix variable
On the home screen of the calculator, type in the multiplication to solve for
calling up each matrix variable as needed.
An invertible matrix has the property
See
[link] .
Use matrix multiplication and the identity to find the inverse of a
matrix. See
[link] .
The multiplicative inverse can be found using a formula. See
[link] .
Another method of finding the inverse is by augmenting with the identity. See
[link] .
We can augment a
matrix with the identity on the right and use row operations to turn the original matrix into the identity, and the matrix on the right becomes the inverse. See
[link] .
Write the system of equations as
and multiply both sides by the inverse of
See
[link] and
[link] .
We can also use a calculator to solve a system of equations with matrix inverses. See
[link] .
Section exercises
Verbal
In a previous section, we showed that matrix multiplication is not commutative, that is,
in most cases. Can you explain why matrix multiplication is commutative for matrix inverses, that is,
If
is the inverse of
then
the identity matrix. Since
is also the inverse of
You can also check by proving this for a
matrix.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature