I `A=[x,y,z], B=[(a,h,g),(h,b,f),(g,f,c)] and C=[x,y,z]^T, then ABC` is (A) not defined (B) a `1xx1` matrix (C) a `3xx3` matrix (D) none of these

If A=[ x y z],B=[(a,h,g),(h,b,f),(g ,f,c)],C=[alpha beta gamma]^T then ABC is

The order of [x,y,z],[(a,h,g),(h,b,f),(g,f,c)],[(x),(y),(z)] is (A) 3x1 (B) 1xx1 (C) 1xx3 (D) 3xx3

If A,B,C are matrices such that A=[x y z], B=[[a,h,g] , [h, b, f] , [g, f, c]] and C=[[x], [y], [z]] then find ABC

If for the matrix A ,\ A^3=I , then A^(-1)= (a) A^2 (b) A^3 (c) A (d) none of these

If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is: (a) . 0 (b) . 1 (c) . 100 (d) . none of these

If a ,b ,c are in G.P. and a^(1//x)=b^(1//y)=c^(1//z), then x y z are in AP (b) GP (c) HP (d) none of these

Consider a system of linear equation in three variables x,y,z a_1x+b_1y+ c_1z = d_1 , a_2x+ b_2y+c_2z=d_2 , a_3x + b_3y + c_3z=d_3 The systems can be expressed by matrix equation [(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)][(x),(y),(z)]=[(d_1),(d_2),(d_3)] if A is non-singular matrix then the solution of above system can be found by X = A^(-1)B , the solution in this case is unique. if A is a singular matrix i.e. then the system will have no solution (i.e. it is inconsistent) if Where Adj A is the adjoint of the matrix A, which is obtained by taking transpose of the matrix obtained by replacing each element of matrix A with corresponding cofactors. Now consider the following matrix. A=[(a,1,0),(1,b,d),(1,b,c)], B=[(a,1,1),(0,d,c),(f,g,h)], U=[(f),(g),(h)], V=[(a^2),(0),(0)], X=[(x),(y),(z)] The system AX=U has infinitely many solutions if :

Let A = { b,d,e,f }, B = { c,d,g,h} and C = {e,f,g,h} .Find : ( A- B ) uu (B-A)

If x, y, z are in G.P. and a^x=b^y=c^z , then (a) logba=log_ac (b) log_cb =log_ac (c) log_ba=log_cb (d) none of these

Consider a system of linear equation in three variables x,y,z a_1x+b_1y+ c_1z = d_1 , a_2x+ b_2y+c_2z=d_2 , a_3x + b_3y + c_3z=d_3 The systems can be expressed by matrix equation [(a_1,b_1,c_1),(a_2,b_2,c_2),(c_1,c_2,c_3)][(x),(y),(z)]=[(d_1),(d_2),(d_3)] if A is non-singular matrix then the solution of above system can be found by X = A^(-1)B , the solution in this case is unique. if A is a singular matrix i.e. then the system will have no unique solution if no solution (i.e. it is inconsistent) if Where Adj A is the adjoint of the matrix A, which is obtained by taking transpose of the matrix obtained by replacing each element of matrix A with corresponding cofactors. Now consider the following matrix. A=[(a,1,0),(1,b,d),(1,b,c)], B=[(a,1,1),(0,d,c),(f,g,h)], U=[(f),(g),(h)], V=[(a^2),(0),(0)], X=[(x),(y),(z)] If AX=U has infinitely many solutions then the equation BX=U is consistent if