Teaching Kids Programming – Linear Algebra: Using Matrix to Solve Equations of X and Y

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Given the following two equations:

We can work on the X or Y in one equation and then substitue it in another equation. For example: from Equation 1, we know and we can plug in x into the second equation.

Linear Algebra: Using Matrix to Solve Equations of X and Y

Let’s put the coefficients of the above equations into the following matrix:

And then we can transform the above equations of x and y into the following matrix multiplication equation:

How to Multiply Two Matrix?

Remember the multiplication rule for Matrix A times B: dot product of the rows of A with the columns of B. Thus, if the Matrix dimension for A is rows1, cols1, and the Matrix B has dimension rows2, cols2, then cols1 = rows2.

For example:

In general for Matrix Multiplication.

Identity Matrix

Identity Matrix (IM) is the Matrix with all ones in the diagonals and zeros elsewhere. For example, the following is a 2×2 Identity Matrix:

With the above matrix multiplication rules, we know that: for Matrix A, where I is the identity matrix.

How to Get Inverse of Matrix?

The inverse of a Matrix A is denoted as such that: where I is the identity matrix.

We want to find out the x in matrix equation thus we can multiply the Inverse of Matrix in both sides:

which becomes and then

For a 2×2 Matrix:

The inverse for Matrix A is:

where is called the determinant for 2×2 Matrix.

Let’s practice above to solve the original equations:

Thus, for the original equations: the solutions are and

–EOF (The Ultimate Computing & Technology Blog) —

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