If `a,b, c, lambda in N`, then the least possible value of `|(a^(2)+lambda, ab,ac),(ba,b^(2)+lambda,bc),(ca, cb, c^(2)+lambda)|` is

Prove that, abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)) =4 a^2b^2c^2 .

abs([-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]) = 4a^2.b^2.c^2

Prove that |[-a^(2),ab,ac],[ba,-b^(2),bc],[ca,cb,-c^(2)]|=4a^(2)b^(2)c^(2)

If vec a and vec b are two vectors and lambda>0, then the least value of (1+lambda)|vec a|^(2)+(1+(1)/(lambda))|vec b|^(2) is

If p lambda^(4) + q lambda^(3) + r lambda^(2) + s lambda + t = |{:(b^(2)+c^(2), a^(2) + lambda , a^(2) + lambda),(b^(2)+lambda,c^(2)+a^(2),b^(2)+lambda),(c^(2)+lambda,c^(2)+lambda,a^(2)+b^(2)):}| is an identity in lambda wherep, q, r,s , t are constants, then the value of t is

If x^(n)-1 is divisible by x-lambda, then the least prositive integral value of lambda is 1 b.3 c.4 d.2

If x^n-1 is divisible by x-lambda, then the least prositive integral value of lambda is 1 b. 3 c. 4 d. 2

If |(a^2+lambda^2, a b+clambda, ca-blambda), (a b-clambda, b^2+lambda^2, b c+a), (ca+blambda, bc-alambda, c^2+lambda^2)| |(lambda, c, -b), (-c,lambda, a), (b,-a,lambda)|=(1+a^2+b^2+c^2)^3 , then he value of lambda is a. 8 b. 27 c. 1 d. -1

Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2