determinant of a matrix 3x3

At this point you may have noticed that finding the determinant of a matrix larger than 2x2 becomes a long ordeal, but the logic behind the process remains the same and so the difficulty is similar, the only key point is to keep track of the operations you are working through, even more with even larger matrices than a 3x3.The determinant of a 3x3 matrix shortcut method is a clever trick which facilitates the computation of a determinant of a large matrix by directly multiplying and adding (or subtracting) all of the elements in their necessary fashion, without having to pass through the matrix expansion of the first row and without having to evaluate secondary matrices' determinants.The whole process of how to evaluate the determinant of a 3x3 matrix using the shortcut method can be seen in the equation below:When computing the determinant of an nxn matrix (in this case a 3x3 matrix) as shown above, notice we first rewrite the matrix accompanied by a repetition of its two first columns now written outside to the right hand side.Then, the determinant value will be the result of the subtraction between addition of products from all of the down-rightward multiplications and the down-leftward multiplications. Remember we will look at that complete topic in a later lesson called: There are two methods for finding the determinant of a 3x3 matrix: the general method and the shortcut method. To understand determinant calculation better input any example, choose "very detailed solution" option and examine the solution.

Be warned, this gets very tedious by hand!All tip submissions are carefully reviewed before being published Reduce this matrix to row echelon form using elementary row operations so that all the elements below diagonal are zero. In that way, we can resolve systems of linear equations by Knowing that, this lesson will focus on the process for evaluating the determinant of a 3x3 matrix and the two possible methods to employ.By using the knowledge that a matrix is an array containing the information of a linear transformation, and that this array can be conformed by the coefficients of each variable in an equation system, we can describe the function of a determinant: a determinant will scale the linear transformation from the matrix, it will allow us to obtain the inverse of the matrix (if there is one) and it will aid in the solution of systems of linear equations by producing conditions in which we can expect certain results or characteristics from the system (depending on the determinant and the type of linear system, we can know if we may expect a unique solution, more than one solution or none at all for the system).But there is a condition to obtain a matrix determinant, the matrix must be a square matrix in order to calculate it. It clears my doubts and difficulties. "

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