1.

By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k)

Answer»

SOLUTION :`|[y+K,y,y],[y,y+k,y],[y,y,y+k]|`
`|[3y+k,y,y],[3y+y,y+k,y],[3y+y,y,y+k]|(byC_1rarrC_2+C_3)`
`=(3y+k)|[1,y,y],[1,y+k,y],[1,y,y+k]|`
`(3y+k)|[1,y,y],[0,k,0],[0,0,k]|`(by`R_2rarrR_2-R_1`and`R_3rarrR_3-R_1`)
`=(3y+k)k^2=k^2(3y+k)`


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