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# How to Solve Matrix Problems?

TopIn mathematics, collection of elements that are arranged in form of rows and columns is known as matrix. Now we will see how to solve matrix problems. Suppose we have a 3 X 3 matrix:
|4 2 5|
|1 5 3|
|3 8 2|
In this example vertical lines are called as columns of matrix and horizontal lines are known as rows of matrix. Now we will see steps to solve matrix.
Step 1: To solve the matrix we choose the first element of first row and column and then avoid first row and column and find the difference between cross multiplication of remaining elements and multiply it by the first element. For example: using above matrix we can write it as:
= 4 (5 * 2 – 8 * 3);
Step 2: Then we choose the second element of first row and second column and avoid first row and second column and find the difference between cross multiplication of remaining elements and multiply it by the second element. For example: using the above matrix we can write it as:
= 2 (1 * 2 – 3 * 3);
Step 3: Then we apply the same procedure with the third element of first row and third column. So we can write it as:
= 5 (1 * 8 – 3 * 5);
Step 4: Then we add first and last column and subtract middle column. So we can write it as:
= 4 (5 * 2 – 8 * 3) + 2 (1 * 2 – 3 * 3) - 5 (1 * 8 – 3 * 5), now we can simplify this matrix. On further solving we get:
= 4 (10 – 24) + 2 (2 – 9) – 5 (8 – 15);
= 4 (-14) + 2 (-7) – 5 (-7);
= - 56 – 14 + 35 = -35;
This is how we solve a matrix.