A matrix `X` has `a+b` rows and `a+2` columns while the matrix `Y` has `b+1` rows and `a+3` columns. Both matrices `X Y` and `Y X` exist. Find `a` and `b` . Can you say `X Y` and `Y X` are of the same type? Are they equal.

The matrix A has x rows and (x+5) column. If the matrix B has y rows and (11-y) columns & both A Ba n dB A exist, then x=8 (b) x=3 y=6 (d) y=8

Matrix A has x rows and x+5 columns. Matrix B has y rows and 11-y columns. If both AB and BA exist, then the ordered pair (x, y) is

Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and 11 - n columns. If both AB and BA exist, then (A) AB and BA are square matrix (B) AB and BA are of order 8 xx 8 and 3 xx 13 , respectively (C) AB=BA (D) None of these

Matrix X has r rows and c columns, and matrix Y has c rows and d columns, where r, c and d are different. Which of the follwing statements must be true? I. The product YX exists. II. The product of XY exists and has r rows and d columns. III. the product XY exists and has c rows and c columns.

The function y=alogx+b x^2+x has extreme values at x=1 and x=2 . Find a and b .

The expressions ax + by has value 7 when x= 2 and y=1 . It has value 1 when x=-1 and y =1 . Find a and b.

Given the matrices A and B as A=[(1,-1),(4,-1)] and B=[(1,-1),(2,-2)] . The two matrices X and Y are such that XA=B and AY=B , then find the matrix 3(X+Y)

For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

Find matrices X and Y , if X+Y=[(5, 2),( 0, 9)] and X-Y=[(3, 6),( 0,-1)] .