Related InterviewSolutions

• Show that all positive integral powers of a symmetric matrix aresymmetric.
• If A is a skew-symmetric matrix and `n`is an odd natural numbr, write whether `A^n`is symmetric or skew-symmetric or neither of the two.
• Show that the matrix `B^TA B`is symmetric or skew-symmetric according as A is symmetric orskew-symmetric.
• A matrix which is both symmetric as well as skew-symmetric is a nullmatrix.
• Express the matrix `[3-2-4 3-2-5-1 1 2]`as the sum of a symmetric and skew-symmetric matrix.
• The sales figure of two car dealers during January 2013 showed thatdealer A sold 5 deluxe, 3 premium and 4 standard cars, while dealer B sold 7deluxe, 2 premium and 3 standard cars. Total sales over the 2 month period ofJanuary-February revealed that dealer A sold 8 deluxe 7 premium and 6standard cars. In the same 2 month period, dealer B sold 10 deluxe, 5 premiumand 7 standard cars. Write 2 x 3 matrices summarizing sales data for Januaryand 2 month period for each dealer.
• If `A ,Ba n dC`three matrices of the same order, then prove that`A=B rArr A+C=B+C`
• Find the value of `lambda,`a non-zero scalar, if `lambda[1 0 2 3 4 5]+2[1 2 3-1-3 2]=[4 4 10 4 2 14]`
• If `A`is a square matrix, using mathematical induction prove that `(A^T)^n=(A^n)^T`for all `n in Ndot`
• In a certain city there are 30 colleges. Each college has 15 peons, 6clerks, 1 typist and 1 section officer. Express the given information as acolumn matrix. Using scalar multiplication, find the total number of posts ofeach kind in all the colleges.