trace

Let A be an n×n matrix over the set of all real numbers R. Let B be a matrix obtained from A by swapping two rows. Which of the following statements is/are TRUE?

Consider the following two statements with respect to the matrices A m $$\times$$ n , B n $$\times$$ m , C n$$\times$$ n and D n $$\times$$ n . Statement 1 : tr(AB) = tr(BA) Statem...

Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trac...

Consider a matrix $$A = u{v^T}$$ where $$u = \left( {\matrix{ 1 \cr 2 \cr } } \right),v = \left( {\matrix{ 1 \cr 1 \cr } } \right).$$ Note that $${v^T}$$ denotes the transpose of $...

Let $$A$$ be $$n\,\, \times \,\,n$$ real valued square symmetric matrix of rank $$2$$ with $$\sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {A_{ij}^2 = 50.} } $$ Consider the followi...

Consider the following $$2 \times 2$$ matrix $$A$$ where two elements are unknown and are marked by $$a$$ and $$b.$$ The eigenvalues of this matrix ar $$-1$$ and $$7.$$ What are th...

Which one of the following statements is TRUE about every $$n\,\, \times \,n$$ matrix with only real eigen values?

Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right]\,\,$$ If the eigen values of $$A$$ are $$4$$ and $$8$$, then

Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right].$$ If the eigen values of $$A$$ are $$4$$ and $$8$$ then

Consider the following C functions: int f1(int n){ if(n == 0 || n == 1){ return n; } return (2 * f1(n - 1) + 3 * f1(n - 2)); } int f2(int n){ int i; int X[N], Y[N], Z[N]; X[0] = Y[...

Consider the following C function definition int Trial (int a, int b, int c) { if ((a > = b) && (c < b)) return b; else if (a > = b) return Trial (a,c,b); else return Trial (b,a,c)...