If A=[{:(3,-2," "0),(-5," "7,sqrt(2)):}]...

If `A=[{:(3,-2," "0),(-5," "7,sqrt(2)):}],` find (-A) and verify that
`A+(-A)=(-A)+A=0.`

Text Solution

Verified by Experts

Clearly, we have:
`(-A)=[{:(-3," "2," "0),(5,-7,-sqrt(2)):}]`
`A+(-A)=[{:(3,-2,0),(-5," "7,sqrt(2)):}]+[{:(-3," "2," "0),(5,-7,-sqrt(2)):}]`
`=[{:(3+(-3),-2+2," "0+0),(-5+5,7+(-7),sqrt(2)+"("-sqrt(2)")"):}]=[{:(0,0,0),(0,0,0):}]=O.`
And, `(-A)+A=[{:(-3," "2," "0),(5,-7,-sqrt(2)):}]+[{:(3,-2," "0),(-5," "7,sqrt(2)):}]`
`=[{:(-3+3,2+(-2)," "0+0),(5+(-5),-7+7,-sqrt(2)+sqrt(2)):}]=[{:(0,0,0),(0,0,0):}]`
Hence, `A+(-A)=(-A)+A=O.`

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