SOLUTION: Solve the following questions: (a) Find curl of (xyz)i + (xy^2)j + (yz)k? (b) Find graidient of (xyz)i + (5xz^2)k - (3xz)k? (c) If determinant of matrix A = 3 and determin

Question 1172353: Solve the following questions:
(a) Find curl of (xyz)i + (xy^2)j + (yz)k?
(b) Find graidient of (xyz)i + (5xz^2)k - (3xz)k?
(c) If determinant of matrix A = 3 and determinant of matrix B = 2 where A and B are 4x4 matrices. Find the determinant of 2 times of inverse of product of matrices A and B i.e. Find determinant of 2 times inverse of A.B?
(d) If A is square matrix of order 2x2 then how many possibile ways are there to construct nilpotent matrix of order 2x2?
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

(0)   When a person asks "solve the question", it means that this person NEVER read from any textbook in Math
        (neither in English NOR in his (or her) native language) and knows equally NEITHER English NOR Math,
        NOR his (or her) native language.

(a)   If you don't know the definition of curl as a determinant, then open any relevant textbook on Multivariable Calculus
        (to which your question does relate) and learn it from there.

        If, in opposite, you are familiar with this definition, use it.

(b)   I am 129% sure that the formula is written incorrectly in this part of your post.

(c)   From elementary properties of determinant, the answer is    = .

(d)   More than million ways. More precisely, infinitely many ways.

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