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if A=[{:(3,-1,2),(0,5,-3),(1,-2,7):}]and...

if `A=[{:(3,-1,2),(0,5,-3),(1,-2,7):}]and B=[{:(1,0,0),(0,1,0),(0,0,1):}],`find whether AB=BA or Not .

Text Solution

Verified by Experts

The correct Answer is:
N/a
No ,Of columns in A=No of Rows InB .
`therefore `ABExists.
`AB=[{:(3,-1,2),(0,5,-3),(1,-2,7):}][{:(1,0,0),(0,1,0),(0,0,1):}]`
`=[{:(3.1+00,0+1(-1)+0,0+02.1),(0+0+0,0+1.5+0,0+0+(-3).1),(1.1+0+0,0+1.(-2)+0,0+0+7.1):}]`
`=[{:(3,-1,2),(0,5,-3),(1,-2,7):}]`
Now No of columns inB =No. of rows in A
` Therefore ` BA exists .
`thereforeBA=[{:(1,0,0),(0,1,0),(0,0,1):}][{:(3,-1,2),(0,5,-3),(1,-2,7):}]`
`=[{:(1.3+0+0,1(-1)+0+0,1.2+0+0),(0+0+0,0+1.5+0,0+1(-3)+0),(0+0+1.1,0+0+1(-2),0+0+1.7):}]`
`=[{:(3,-1,2),(0,5,-3),(1,-2,7):}]`
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