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True or false? 1. If det(A)=0 then A=0. 4. If det(A) = 3  then det(2A) = 6. 5. If A is...

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bobby9901 | Student, College Freshman | (Level 1) Salutatorian

Posted April 26, 2013 at 2:08 PM via web

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True or false?

1. If det(A)=0 then A=0.

4. If det(A) = 3  then det(2A) = 6.

5. If A is a 2x2 matrix with zero determinant, then one column of A must be a multiple of the other one.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 27, 2013 at 3:52 AM (Answer #1)

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Det(A)=0 does not mean A=0

`A=[[1,0],[1,0]]`

`|A|=0 `

`` But  A`!=0`

`A=[[1,0],[0,1]]`

`|A|=1`

`2A=[[2,0],[0,2]]`

`|2A|=4`

`!=2` det(A)

`A=[[2,1],[2,1]]`

`|A|=0`

One column is multiple of the other.

We need more observation.

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