Subtracting both sides of the equation by the leftmost matrix in the To solve this equation, we want to rearrange In this example, we need to solve a matrix equation to find the unknown Solve the following matrix equation for □: Hence, this gives the solution to the matrix equation □ □ = □.Įxample 1: Solving a Matrix Equation Involving a 3 × 3 Matrix Since □ □ = □ , this equation simplifies to Respectively, we need to multiply from the left by □ on Now, to solve the matrix equation □ □ = □, where Given aĭ e t □ ≠ 0, the inverse matrix □ is Of a square matrix exists if its determinant is not equal to zero. How to solve a matrix equation of the form □ □ = □ using the □ □ = □, where □ is a square matrix of order □ linear equations as one matrix equation of the form We will see further below in this explainer how to write these systems of The matrix inverse so that we can easily program a computer to perform this One of the most widely usedĪpplications of matrix operations is to formalize this process by means of This is where the matrix method comes in. But if we want to program a computer to perform this task for us, we need a Even withĪ system of three equations, this process is time consuming to solve by hand. We can solve a system of linear equations, which are also called simultaneousĮquations, using the substitution or elimination methods, but these methodsīecome convoluted when the number of equations are more than two. Using the inverse of the matrix of coefficients. In this explainer, we will learn how to solve a system of three linear equations
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