Are the following statements true or false? Here A is an n by n square matrix. 1. If A is not invertible then the system A(vector x) = vector b has infinitely many solutions. 2.The zero matrix is...

 Are the following statements true or false? Here A is an n by n square matrix.

1. If A is not invertible then the system A(vector x) = vector b has infinitely many solutions.

2.The zero matrix is invertible.

3.The product of two elementary matrices is an elementary matrix.

4. If A is invertible then so is A^T.

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pramodpandey | College Teacher | (Level 3) Valedictorian

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1. Not true

let

2x+4y=9

4x+10y=11

`[[2,5],[4,10]][[x],[y]]=[[9],[11]]`

`AX=b`

A is not invertible,

Also it has no solution.

2. Not true.

4. True.

3. True

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