Determine whether each 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 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. false, adding a multiple of one column to another changes the value of the determinant by the multiple of the minor. 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. false, row-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. true, column-equivalent matrices are matrices that can be obtained from each other 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. (c) if one row of a square matrix is a multiple of another row, then the determinant is 0. 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. 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, 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, 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.