Question

let A be 3x3 matrix with (2,0,-1) as first row (4,0,-2) as second row and (0,0,0) as third row .let T be multiplication by A find basis for range of T

Answer 1

2 0 -1
4 0 -2
0 0 0 ?

Answer 2

yes this is my 3x 3 matrix

Answer 3

o -2 4 -2 4 0
(2) 0 0 (-0) 0 0 +(-1) 0 0

Answer 4

sir, please explain i am not getting your vpoint

Answer 5

I,m not done yet

Answer 6

read this is hard for explain

Answer 7

[(2)(0*0)-(0*-2) (-0)(0*4)-(0*-2) (-1)(0*4)-(0*0)]
[(2*2) ( ............... time 0 all cancel..........]
=4

Answer 8

first use sign + - +

Answer 9

the first row 2 0 -1 , (2 is positive sign) ,( 0 negative sign) , ( -1 positive sign)

Answer 10

if you are trying to find a basis for the range of the transformation, you should row reduce the matrix, and find the pivots. those pivots indicate which columns are linearly independent and form a basis for the range of T. I dont know of anyway to use the determinant of a matrix to find a basis for the range.....although i wont claim there isnt a way. i just dont know of it if there is.

Answer 11

(2) minor is : 0 -2
0 0
you cross (0*0)-(0*-2)

Answer 12

0-(-2)=2
2*2=4

Answer 13

did you get it?

Answer 14

(-0) minor is : 4 -2
0 0
you cross (4*0)-(0*-2)
(-0)* 0 -(-2) = -0*2
= 0

Answer 15

4 0
+(-1) 0 0
you cross and time=
(-1)* (4*0)-(0*0)
( -1*) 0 -0 = -1*0
= 0

Answer 16

the answer is 4

Answer 17

or you can solve by use Diagonals,

Answer 18

not hard to solve, but I don't know how to explain on the chat, my son love to solve Matrices

Answer 19

i dont mean to sound rude, but I dont see how this solves his problem at all. His problem was asking for a basis for the range of T, not the determinant of A.

Answer 20

than I don't know

Answer 21

i posted this further up, here is the solution:

Answer 22

@sir joemath the answer in my book is (1,2,0) i got your point very well but the answer in book is different from yours

Answer 23

ah, we have the same answer, their answer is mine divided by 2. the concept is like reducing fractions:
\[\frac{2}{4} = \frac{1}{2}\]
i guess they want to pull out any common factors between the numbers in their basis? i dont see why you would want to do that, but hey, when in Rome.

Answer 24

@ sir joemaththanks thanks thanks sir for answer nancy lam was telling me about determinent but i was asking about range which you told me

Answer 25

[(2)(0*0)-(0*-2) (-0)(0*4)-(0*-2) (-1)(0*4)-(0*0)]
[(2*0) ( ............... time 0 all cancel..........] =0
I calculator wrong is o

Answer 26

it was just a misunderstanding, it happen to the best of us, ive done it a bajillion times lol

Answer 27

The basis for the range is the same as the basis for the column space if I'm not mistaken. . .

Answer 28

thats correct :)