In this lecture we derive several useful properties of the determinant. In order to fully understand this lecture you need to remember the main results derived in the lecture on the determinant of an elementary matrix. Determinant of a triangular matrixThe first result concerns the determinant of ...
How do you find the determinant of a triangular matrix? Compute the determinant of the following matrix. \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 &9 \end{bmatrix} Compute the determinant of the matrix: \begin{bmatrix} 2 & 1 &-1 \\ 2& 0 & -1 \\ -2 &-3 & ...
Let be a small number. Then (27) where is the matrix trace of . The determinant takes on a particularly simple form for a triangular matrix (28) Important properties of the determinant include the following, which include invariance under elementary row and column operations. 1. Switchi...
is a square matrix. Block matrices whose off-diagonal blocks are all equal to zero are called block-diagonal because their structure is similar to that ofdiagonal matrices. Not only the two matrices above are block-diagonal, but one of their diagonal blocks is an identity matrix. We will cal...
a. 1.决定物的;决定因素的 英语解释 having the power or quality of deciding a square matrix used to solve simultaneous equations a determining or causal element or factor the site on the surface of an antigen molecule to which an antibody attaches itself ...
There are many methods used for computing the determinant. Some matrices, such as diagonal or triangular matrices, can have their determinants computed by taking the product of the elements on the main diagonal. For a 2-by-2 matrix, the determinant is calculated by subtracting the reverse diagon...
If the determinant of a square matrix is non-zero, then the matrix is called a ___matrix. View Solution Which of the following is a symmetric matrix? (A) a null matrix (B) a triangular matrix (C) an idenity matrix (D) a diagonal matrix View...
Assume that A and B are n×n matrices with detA=8 and detB=−9. Find the indicated determinant. det(B−1A) Determinant: The determinant of a particular matrix is connected to that matrix and it is calculated for square matrices. However, when ...
For example, det can produce a large-magnitude determinant for a singular matrix, even though it should have a magnitude of 0. Algorithms det computes the determinant from the triangular factors obtained by Gaussian elimination with the lu function. [L,U] = lu(X) s = det(L) % This is ...
matrix algebra/ fuzzy matrix determinantco-t normssquare matricestriangular normtriangular conorm/ B0210 Algebra B0250 Combinatorial mathematics C1110 Algebra C1160 Combinatorial mathematicsWe study determinants of square matrices over the interval [0,1] when ordinary multiplication is replaced by a ...