PreCalculus
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All Systems Go!
Posted on May 6, 2010
Topic: Vectors and Matrices
Students learn about inverse matrices in the context of encoding/decoding secret messages and then use inverse matrices to solve systems of equations.
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Activity Key Steps:
In Problem 1, students use the concept of an inverse matrix to explore encoding and decoding secret messages.
Students will find the inverse of the encoding matrix and confirm that multiplying the encoding matrix by the decoding matrix results in the identity matrix.
Students will then decode the matrix on the encoded message to check that they are able to retrieve the original message.
In Problem 2, students use inverse matrices to solve a system of equations. They use the Calculator application to multiply the inverse of the coefficient matrix by the constant matrix to obtain the solution.
Problem 3 gives students the opportunity to find the equation of a parabola using system of equations and matrices. They find the equation of the parabola that passes through three specific points.
They can confirm their solution by graphing the equation in and the plot each coordinate to see if it passes through the three points.
At the end of this activity, students will be able to compute the product of any pair of matrices and the inverse of a square non-singular matrix. They will also be able to solve a linear system of n equations in n variables by computing the inverse of the coefficient matrix.