After evaluating the summation, we will find that the resulting determinant will have columns that are linearly dependent, leading to a determinant value of zero. Conclusion Thus, the value of n∑r=1Δr is independent of x,y,z,n and equals zero. Show More | ShareSave ...
d) (a,b,c) where a⋅b=0. Subspaces: Suppose V is a vector space defined over a field F. A subset W of V is a subspace if it forms a vector space under the same operations as V. In order to test this we usually us...
If a×b are two nonzero vectors, then a and b are orthogonal. Orthogonal of Two Vectors: If a is orthogonal to b, then the angle between a and b is π2. This is valid if and only if the dot product of a and b is zero. Answer...
11. Ifa,b,c∈R−{0}, such thata≠b≠c, then the matrix⎡⎢ ⎢⎣0(a−b)3(a−c)3(b−a)30(b−c)3[c−a)3(c−b)30⎤⎥ ⎥⎦is (A) symmetric (B) singular (C) non-singular (D) invertible View Solution ...
If A is a square matrix such that AA equals the zero matrix, then A must equal the zero matrix. True or false? The eigenvalues of a matrix are on its main diagonal. True False If a square matrix B is invertible, then its inverse has zero determinant. A. True B. False Let A ...
Answer to: Prove that, if sum of all elements in all rows of a matrix is zero, then the determinant of the matrix is also zero. By signing up,...
A matrix is an arrangement of numbers settled in square or rectangle. Number of row cross number of column is called the order of the matrix. For the matrix having same number of row and column is called square matrix. ...
Determine whether the following statement is True or False. A square matrix and its transpose have the same determinant. a. True b. False If A, B are symmetric matrices and AB = BA, then AB is also symmetric. True False If A is positive def...
True or False: If A is an n by n matrix and AB = O, then B = O. If a square matrix B is invertible, then its inverse has zero determinant. A. True B. False If a square matrix A is invertible, then the reduced row echelon form of A is ...
A vector is a quantity that has both magnitude and direction. A given set of vectors is said to be linearly independent if the determinant of the matrix formed by taking vectors as the columns is non-zero.Answer and Explanation: Become a member and unlock all Study Answers Start today. ...