12. [-13.22 Points] DETAILS LARLINALG8 3.2.038. ASK YOUR TEACHER Determine whether ebch statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant. False, adding a multiple of one column to another changes the value of the determinant by the multiple of the minor. True, adding a multiple of one column to another changes only the sign of the determinant. False, adding a multiple of one column to another changes the sign of the determinant. O False, adding a multiple of one column to another does not change the value of the determinant. (b) Two matrices are column-equivalent when one matrix can be obtained by performing elementary column operations on the other. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary row operations on the other. False, row-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other. O False, row-equivalent matrices are matrices that can be obtained from each other by performing elementary row operations on the other. O True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other. (c) If one row of a square matrix is a multiple of another row, then the determinant is 0. False, this is true for columns, because you can achieve a row of all zero’s by adding a multiple of one row to another which does not change the determinant of the matrix. False, this is true for columns, because you can achieve a column of all zero’s by adding a multiple of one column to another which does not change the determinant of the matrix. False, you can achieve a row of all zero’s by adding a multiple of one row to another which changes the determinant of the matrix. O True, you can achieve a row of all zero’s by adding a multiple of one row to another which does not change the determinant of the matrix.

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