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 study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
