## TiNspire: CoFactors , Determinant , A as Product of Elementary Matrices

To Find a Determinant given CoFactors in a Row use Linear Algebra Made Easy at www.TiNspireApps.com and enter your quadratic Matrix and selected Row as follows:

When selecting Row2 we get the following CoFactors and of course the same determinant:

To Express a quadratic Matrix as a Product of Elementary Matrices we simply keep track of the RREF Operations when finding its Inverse Matrix. See below:

and finally

Voila !

## Gauss Seidel Method – Step by Step – using the TiNspire CX CAS

Say we have to solve the following system of equations using the Gauss Seidel method.

We just launch the Numerical Analysis Made Easy app at www.TiNspireApps.com , go to Menu option A 2 and enter the problem as shown below using matrix A and matrix B:

and

until we finally arrive at the last step :

## ▷Orthogonal Projection of v onto u1,u2 using the TiNSpire – Linear Algebra Made Easy

Say you need to find the orthogonal projection of v onto W the subspace of R^3  .

You pull out your TiNspire and launch the Linear Algebra Made Easy app from www.ti-nspire-cx.com and enter as follows:

.

Now, just lean back and view the steps

until the final answer shows. Sweet!

## ▷Gauss Jordan Elimination / Row Echelon – Step by Step – using the TiNSpire CX

Gauss Jordan Elimination is a pretty important topic in Linear Algebra.

So, it would be great to see steps when performing the procedure, also called Reverse Row Echelon method. It seems there is a continental divide in its proper naming.

Once you can pull out your handy TiNspire and launch the Linear Algebra Made Easy app from www.tinspireapps.com just enter your matrix as shown below:

Notice that first the forward Gauss Elimination Method is performed, aka Row Echelon Method.

Lastly, the Reverse Row Echelon Method gives the final solution, which appears in the most right column. Voila.

## Span of Vectors or Polynomials with the TiNspire using Linear Algebra Made Easy

To check if vectors span R^2, R^3 , .. just select “Span of Vectors” in the Menu of
the Linear Algebra Made Easy app at www.TiNspireApps.com  as shown below:

Next, enter Vectors as rows in matrix, use ; to end row(vector).

Using RREF to determine the rank of matrix we can conclude if
the vectors entered span R^2. Here they do.

Optionally, enter a vector in the 2. box to check if it part of the
span of the vectors entered in the 1. box .

Note: to view steps on the RREF computation, just enter the
vectors under the RREF option.

Similar to checking the SPAN of Vectors you can also check the
SPAN of polynomials by entering the polynomials coefficients
as row coefficients as shown below.
Optionally, enter a polynomial in the 2. box to check if it part of the
span of the polynomials entered in the 1. box .

## Compute Determinant for 2×2, 3×3, 4×4, 5×5 Matrix via Cofactors – Step by Step – using TiNspire’s Linear Algebra Made Easy

There is a number of ways to compute determinants of square matrices depending on their dimensions.

Determinants of 2×2 and 3×3 matrices can simply be computed using their set formulas as seen below:

Determinants of 4×4 and higher matrices actually take advantage of determinants found for smaller square matrices using Cofactors as illustated below. As usual, nicely laid out with every step along the way until the final answer shows.

https://www.tinspireapps.com/?a=LAME

## Not only are these apps a life saver but the costumer service was even more impressive.

They are incredibly user friendly and helped me a ton, I just got a 100 on my linear test using this app!
Not only are these apps a life saver but when I had a question regarding downloading the apps, the costumer  service  was even more impressive.
I have tried other apps before and had multiple complications with getting the apps to work and when I emailed no one was there to answer or care.
There is no other website or apps  that can even come close to ti89.com and tinspireapps.com,  they are truly unique.
Thank you ti89.com : you’re amazing
JLK

## Linear Algebra Made Easy for the TiNspire now does Step by Step Span and Bases of Vectors and Polynomials

Linear Algebra Made Easy for the TiNspire now does – Step by Step as always –

-Check if Vector is in Span of Basis/Vectors

-Do Vectors span Vector Space and thus form Basis?

-Check if Polynomial is in Span of Basis/Polynomials

-Do Polynomials span Vector Space and thus form Basis?

Combine that with the powerful step by step tools of this app such

-REF and RREF

-Gauss Elimination

-Eigenvalues and Vectors

-Orthonormal Basis and GramS Schmidt Procedure

-LU and QR Decomposition

-Kernel, Range, Nullity, Basis for Nullspace, Rowspace and Columnspace

-Vectors: Cross , Dot Product, Length , Test of Independence, Projection , Distance, Etc

This Linear Algebra App rocks!!!

## Linear Algebra Made Easy is incredible & enjoyable

User feedback today:

The step by step matrix operations, such as Row Echelon, Gauss Elimination etc are incredible

It is very easy to use;

I like the layout and on the Ti-spire since the processor is faster than the 89 it just makes it more enjoyable to use.

My linear algebra professor does allow us to use a CAS calculator and with the Ti-nspire cx CAS with your linear algebra app… Lets just say my fellow students and professor will be amazed with my knowledge and wisdom… and of course the speed at which I solve matrix operations and systems.

C.P.

## Step by Step Linear Algebra app for the Ti-Nspire CAS CX

Overview and Examples : https://youtu.be/uqIRhvqqVDE

Perform 30+ Matrix Computations such as A+B, A-B, k*A, A*B, B*A, A-1, det(A), Eigenvalues, LU and QR – Factorization, Norm, Trace.

• Step by Step – Simplex Algorithm.
• Step by Step – Gaussian Elimination.
• Step by Step – Find Inverse
• Step by Step – Find Determinant
• Step by Step – Row Echelon and Reversal (REF and RREF)
• Step by Step – Gauss and Gauss Jordan Elimination
• Step by Step – Cramer Rule
• Step by Step – EigenValues and EigenVectors.
• Step by Step – Square Root Matrix
• Solve any n by n system of equations.
• Rotation Matrices, Magic Squares and much more.
• Step by Step – Solve AX=B
• Step by Step – OrthoNormal Basis
• Step by Step – Range, Kernel
• Nullity, Null-, Row- and ColumnSpace Basis.
• Cross and Dot Product, UnitVector, Angle between Vectors
• Projection A onto B, Distance A to B, etc …