Please Answer True or false for all questions Answer true or

Please Answer True or false for all questions

Answer true or false  56, 60, 62

Here answer True or false 64,66,68

64:If two matrices of the same size have equal rank , than their reduced form must be identical

68. If the reduced form A* has a row of zeros than so does A

Here answer True or false 6,8,10

Answer true of false 12,14,16,18,20

2. If AD = BD , for nxn matrices A,B,D then A=B

4. If A is symmetric , than -A is skew - symmetric

10. If A and B are nxn invertible matrices , then A+B is invertible .

Answer True or False 12 14, 18.

Solution

56) False. Can have 2 free variables if rank = 1

60) False. subsystem may have dependent solutions

62) True. n represents the columns

64) True. Since no of equations exceed no of variables may be inconsistent.

66) True. row equivalence is performed to find rank only to lowest form

68) False. After reducing only A has zero row. So not necessary that A should have

12) True but has some free variables.

14) True as rank represents no of non zero rows.

16) False max rank can only be 4

18) True since if c = 5 then rank = 1

20)False. This can be true only for square system.

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12) False.

14) False

18) True as matrix cannot be singular and hence has inverse.