Show with the usual notation that for any matrix `A = [a_ij]3xx3`, ` a_11A_11+a_12A_12+a_13A_13 = abs(A)`

Show with the usual notation that for any matrix A = [a_ij]_3xx3 , a_11A_21+a_12A_22+a_13A_23 = 0

For the following determinant |(2,1,3),(3,3,4),(2,1,5)| verify that a_21A_11+a_22A_12+a_23A_13=0

If A=[(cos theta,sin theta,0),(-sin theta,cos theta,0),(0,0,1)] , where A_(11), A_(12), A_(13) are co-factores of a_(11), a_(12), a_(13) respectively, then the value of a_(11)A_(11)+a_(12)A_(12)+a_(13)A_(13)=

Show that the points (5,11) is equidistant from the points (-5,13) and (3,1)

Which of the following is not a subset of the set T? : T = {1, 2, 3, 5, 7, 9, 11, 13}

Fill in the blanks with elements of that set . U = {1, 3, 5,8, 9, 10, 11, 12, 13, 15} A = {1, 11, 13} B= {8, 5, 10, 11, 15} A' = {...................} B' = {................} AnnB = {..........} (A nn B)' = {..............} AuuB = {..........} (A uu B)' = {..............} A' nn B' = {..........} 'A' uu B' = {..............} Verify (A nn B)' = A' uu B' (A uu B)' = A' nn B'

Find the values of x for which the following functionf(x)= x^3 -12 x^2 -144 x + 13 is Increasing

Find the matrix X such that AX=B , where A = [[1,2],[-1,3]] , and B = [[0,1],[2,4]]

Show that the equation: 3x^2+3y^2+12x+18y-11=0 represents a circle.