To explain: Whether the statement “If any row (or any column) of a determinant is multiplied by a nonzero number k , the value of determinant remains unchanged.” is true or false.
Answer to Problem 6AYU
The statement “If any row (or any column) of a determinant is multiplied by a nonzero number k, the value of determinant remains unchanged.” is false.
Explanation of Solution
Given information:
The statement “If any row (or any column) of a determinant is multiplied by a nonzero number k , the value of determinant remains unchanged.”
Consider the provided statement “If any row (or any column) of a determinant is multiplied by a nonzero number k , the value of determinant remains unchanged.”
Consider the matrix,
Recall that for the matrix of order
The determinant is given as
Therefore, determinant of the matrix is given by,
Now, multiply the first row by 2, so new matrix is
Therefore, determinant of the matrix is given by,
Observe that determinant of new matrix is two times the old one.
Therefore, if any row (or any column) of a determinant is multiplied by a nonzero number k , the value of determinant becomes k times.
Thus, the statement “If any row (or any column) of a determinant is multiplied by a nonzero number k, the value of determinant remains unchanged.” is false.
Chapter 11 Solutions
Precalculus
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