Question

ermine whether wachttement is true or false. If a statement is true, glve a reason or site an appropriate statement from the text. If a statement is false, provide an example that shows th (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. 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. True, column-equivalent matrices are matrices that can be obtained from each other 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 (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. 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 o 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. 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

Answer 1

a.option 4

b.option 2

c.option 2
= :] 2-1 = 1 if het us consider matrix square we add 40, to cz then 29 then also determinant = 10 - 9 = 1 so on adding multiple of one column to other column there is no change in valine as well as sign of defuminant. 2 option 4 is correct.

© Column equivalent matrices are obtained by fexoining elementary operations on the other. This statement is True. oplim 2 is correct. Yes, If a row is multiple of another roo then its determinant is zero because you can subtrand that multiple facts and comert the row tozero. nence determinant would be zero. option 2 is correct.
n 2