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