Thus, the kernel of a chemical equation’s coefficient matrix is also the solution to the chemical equation, provided the stoichiometric coefficients are in their simplest, whole number ratios. Solving the equation for is known as computing the null space, or kernel, of the coefficient matrix A. If the coefficient matrix above is denoted by A and the solution vector, then the system follows the homogeneous equation A. Which is equivalent to the matrix setting Reformulating eq 1 for each element in Ac yields the linear homogeneous system Where a denotes the subscript for element A in each term of Ac. Where both sides of the above equation refer to the same element. The first condition for balancing any chemical equation asserts the law of conservation of mass. Where x 1 through x r denote both the term and unknown coefficient for each compound reacting, x r+1 through x p the term and unknown coefficient for each compound being produced, and β the net charge associated with each compound. This manuscript will continually refer to the following chemical equation Ac, where

This contribution introduces a new, calculator-based method, which has potential to alter how balancing redox equations is taught. The major contribution in this report is the linear algebraic representation of the acidic and basic half-reaction procedure. The proposed method is appropriate for undergraduate chemistry classes and perhaps Advanced Placement courses, provided scientific calculators are available. It is the purpose of this work to establish a calculator-based procedure for balancing acidic and basic conditioned redox equations. Balancing chemical equations with linear algebra simplifies the algebraic method however, according to McCoy, “Linear algebra not help balance properly.” Many authors proceeded to disprove this proposition, while others introduced the necessary reformulations of both chemical and redox equations to derive effective linear algebraic methods. Likewise, using algebra to balance redox equations has proven to be even more difficult, allowing other methods such as inspection or half-reactions to be more commonly taught. The algebraic method for balancing chemical equations is traditionally less popular than alternative methods, as the corresponding sets of linear equations are often tedious to equate.

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