`A=[a_(ij)] _(mxxn)` is a square matrix , if :

A =([a_(i j)])_(mxxn) is a square matrix, if (a) m n (c) m =n (d) None of these

Let A=[a_(ij)]_(nxxn) be a square matrix and let c_(ij) be cofactor of a_(ij) in A. If C=[c_(ij)] , then

Let A=[a_(ij)]_(3xx3) be a square matrix such that A A^(T)=4I, |A| lt 0 . If |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|=5lambda|A+I|. Then lambda is equal to

A matrix A=[a_(ij)]_(mxxn) is

If A=[a_(ij)] is a square matrix of order 3 and A_(ij) denote cofactor of the element a_(ij) in |A| then the value of |A| is given by

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) rltmin{m,n} (B) rlemin{m,n} (C) r=min{m,n} (D) none of these

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemin{m,n} (C) rltmin{m,n} (D) none of these

If A=[a_(i j)] is a square matrix of even order such that a_(i j)=i^2-j^2 , then (a) A is a skew-symmetric matrix and |A|=0 (b) A is symmetric matrix and |A| is a square (c) A is symmetric matrix and |A|=0 (d) none of these

If A=[a_(i j)] is a square matrix such that a_(i j)=i^2-j^2 , then write whether A is symmetric or skew-symmetric.

A homogeneous polynomial of the second degree in n variables i.e., the expression phi=sum_(i=1)^(n)sum_(j=1)^(n)a_(ij)x_(i)x_(j) where a_(ij)=a_(ji) is called a quadratic form in n variables x_(1),x_(2) …. x_(n) if A=[a_(ij)]_(nxn) is a symmetric matrix and x=[{:(x_(1)),(x_(2)),(x_(n)):}] then X^(T)AX=[X_(1)X_(2)X_(3) . . . .X_(n)][{:(a_(11),a_(12) ....a_(1n)),(a_(21),a_(22)....a_(2n)),(a_(n1),a_(n2)....a_(n n)):}][{:(x_(1)),(x_(2)),(x_(n)):}] =sum_(i=1)^(n)sum_(j=1)^(n)a_(ij)x_(i)x_(j)=phi Matrix A is called matrix of quadratic form phi . Q. If number of distinct terms in a quadratic form is 10 then number of variables in quadratic form is