Solving simultaneous equations with matrices.



Solving simultaneous equations with matrices.To solve simultaneous equations with matrices it is important to know how matrices multiply together. To multiply a matrix, you must times rows of matrix A by each column within the matrix B and add the corresponding values. (1)Now to adapt this to solve to solve a simultaneous equation the equations must first be rearranged to make it suitable for the operation.?Now, what do we do? Well, the first step is to arrange this into a matrix with all the coefficients of x on the left and coefficients of y on the right of matrix A. Then we formulate matrix X by simply putting x above y. After this, we simply put the solutions into this equation above one another in matrix B (3).Are you still with me? Now that these matrices are set up it can be said that matrix A, multiplied by matrix X gives us Matrix B (3).So if we want to just find out the values for X we can simply divide matrix B by Matrix A. Another way of saying this is matrix B multiplied by the inverse of matrix A (3).But what exactly is the inverse of matrix A. Well it's not as difficult as you may think? In fact, all you have to do is switch the position of a and d, and make the values for b and c negative. Then, multiply each number in the matrix by the inverse of its determinant. (2)This will give you the value for the inverse of matrix A.Now time to multiply the matrices together to find Matrix X. Now as previously stated, to multiply a matrix, you must times rows of matrix A by each column within the matrix B and add the corresponding values. The answers will give you the corresponding values for x and y.Giving youThis will give you the value of x and y. It is important to understand this process if you plan on solving simultaneous equations with several variables as these can be programmed into computer software in order to determine the values of all constants (3).ReferencesIntro to matrix multiplication?(no date) Available at: (Accessed: 9 November 2016).MathsIsFun (2014)?Inverse of a matrix. Available at: (Accessed: 9 November 2016).Matrices -solving two simultaneous equations?(2009) Available at: (Accessed: 9 November 2016). ................
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