Course Linear Algebra Class Name ID ?? (4x9 marks) Mark each statement TRUE or F
ID: 3185875 • Letter: C
Question
Course Linear Algebra Class Name ID ?? (4x9 marks) Mark each statement TRUE or FALSE (1)Every matrix is row equivalent to a unique matrix in redusced echclon fom 2) If A is an mxn matrix and the equation A s is consistent for every in R",then A has m pivot columns 3)L 1If A and B are row equivalent mxn matrices and if the columns of A span R", then so do the columns of B (4)??]lf A and B are nxn matrices, then AB.BA. (5), JIf A is a 4x4 matrixamd the equation Ax-(3 0 1 0), has a unique solution, then A is invertible. (6) L-JIf As 0, then det A 0. (7) ]If A is a 2x 2 matrix with a zero determinant, then one column of A is a multiple of the other (8) L ] If matrix A is invertible, then (adj A)"1 (9)? If A and B are square ard invertible, then AB is invertible, and (AB)-1- A-B-1 1rs
Explanation / Answer
1) The statement is true.
2) The statement is true.
3) The statement is false.
Reason : A and B are row equivalent. So,A can be converted into B by some elementary row operations. But A and B may or may not column equivalent. So, if columns of A spans Rn then columns of B may or may not spans Rn according to column equivalent.
4) The statement is false.
Reason : Matrix multiplication is not commutative.
5) The statement is true.
6) The statement is true.
7) The statement is true.
8) The statement is true.
9) The statement is false.
Reason : A and B must be of same order, otherwise matrix AB does not exist.