To prove: The value of new second order determinant is same as the original one if all entries of either a row or a column are multiplied by a real number k , and the resultant products are added to corresponding entries of either another row or another column.
Explanation of Solution
Given information:
The second order determinant.
Proof:
Consider a second order matrix,
The determinant of above matrix is,
According to the question multiply all entries of row 2 by a real number say k and add the corresponding product to row 1.
Observe that
Hence, it is proved that the value of new second order determinant is same as the original one if all entries of either a row or a column are multiplied by a real number k , and the resultant products are added to corresponding entries of either another row or another column
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