![]() A symmetric matrix has symmetric entries with respect to the main diagonal. ![]() Furthermore, it is possible only for square matrices to be symmetric because equal matrices have equal dimensions. Question 5: What is meant by a symmetric matrix?Īnswer: A symmetric matrix refers to a square matrix whose transpose is equal to it. Question 4: Can we say that a zero matrix is invertible?Īnswer: No, a zero matrix is not invertible. In other words, we can say that a scalar matrix is an identity matrix’s multiple. In a scalar matrix, all off-diagonal elements are equal to zero and all on-diagonal elements happen to be equal. ![]() The various types of matrices are row matrix, column matrix, null matrix, square matrix, diagonal matrix, upper triangular matrix, lower triangular matrix, symmetric matrix, and antisymmetric matrix.Īnswer: The scalar matrix is similar to a square matrix. These rows and columns define the size or dimension of a matrix. Question 2: What is meant by matrices and what are its types?Īnswer: Matrix refers to a rectangular array of numbers. For example, $$ A =\begin$$ is a diagonal matrix is a diagonal matrix A matrix is said to be a row matrix if it has only one row. Some of them are as follows:Ī row matrix has only one row but any number of columns. It didn't look as neat as the previous solution, but it does show us that there is more than one way to set up and solve matrix equations.Different types of Matrices and their forms are used for solving numerous problems. (This one has 2 Rows and 2 Columns) Let us calculate the determinant of that matrix: 3×6 8×4. The matrix has to be square (same number of rows and columns) like this one: 3 8 4 6. In fact it is just like the Inverse we got before, but Transposed (rows and columns swapped over). The determinant is a special number that can be calculated from a matrix. Then (also shown on the Inverse of a Matrix page) the solution is this: The rows and columns have to be switched over ("transposed"): I want to show you this way, because many people think the solution above is so neat it must be the only way.Īnd because of the way that matrices are multiplied we need to set up the matrices differently now. Do It Again!įor fun (and to help you learn), let us do this all again, but put matrix "X" first. Quite neat and elegant, and the human does the thinking while the computer does the calculating. Just like on the Systems of Linear Equations page. Then multiply A -1 by B (we can use the Matrix Calculator again): (I left the 1/determinant outside the matrix to make the numbers simpler) We can solve matrices by performing operations on them like addition, subtraction, multiplication, and so on. The calculations are done by computer, but the people must understand the formulas. It is also a way to solve Systems of Linear Equations. It means that we can find the X matrix (the values of x, y and z) by multiplying the inverse of the A matrix by the B matrix.įirst, we need to find the inverse of the A matrix (assuming it exists!) Calculations like that (but using much larger matrices) help Engineers design buildings, are used in video games and computer animations to make things look 3-dimensional, and many other places. ![]() Then (as shown on the Inverse of a Matrix page) the solution is this: A is the 3x3 matrix of x, y and z coefficients.Which is the first of our original equations above (you might like to check that). Why does go there? Because when we Multiply Matrices we use the "Dot Product" like this:
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