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What is the determinant of a two-by-two matrix?

To find that, you multiply the first element of the first row by the second element of the second row. You also multiply the first element of the second row with the second element of the first row. Then you subtract the products not add them.


Determinant of a 4x4 matrix?

The determinant of a 4x4 matrix can be calculated using various methods, including cofactor expansion or row reduction. The cofactor expansion involves selecting a row or column, multiplying each element by its corresponding cofactor, and summing the results. Alternatively, row reduction can simplify the matrix to an upper triangular form, where the determinant is the product of the diagonal elements, adjusted for any row swaps. The determinant provides important information about the matrix, such as whether it is invertible (non-zero determinant) or singular (zero determinant).


What is the minor of determinant?

The minor is the determinant of the matrix constructed by removing the row and column of a particular element. Thus, the minor of a34 is the determinant of the matrix which has all the same rows and columns, except for the 3rd row and 4th column.


Does doing row operations on a matrix change its determinant?

No.


Does doing row operations of a matrix change its determinant?

No.


If the determinant of a 5x5 matrix delta is the detdelta 5 and the matrix feta is obtained from delta by adding 9 times the third row to the second then detfeta is?

It is the same.


A spreadsheet contains 798 entries in a rectangular array which has 38 rows how many entries are in each row?

Easy! 798 divided by 38 = 21 so da answer is 21 entries in each row


What is the value of the determinant if the corresponding elements of two rows of a determinant are proportional?

If two rows of a determinant are proportional, the value of the determinant is zero. This is because proportional rows indicate that one row can be expressed as a scalar multiple of the other, leading to linear dependence. Consequently, the determinant, which measures the volume of the parallelepiped formed by the rows, collapses to zero.


What is the formula of bordered Hessian matrix?

The bordered hessian matrix is used for fulfilling the second-order conditions for a maximum/minimum of a function of real variables subject to a constraint. The first row and first column of the bordered hessian correspond to the derivatives of the constraint whereas the other entries correspond to the second and cross partial derivatives of the real-valued function. Other than the bordered entries, the main diagonal of the sub matrix consists of entries for the second partial derivatives. All other entries of the sub matrix off of the main diagonal correspond to all combinations of cross partials. Evaluating the determinant of the bordered hessian will allow one to determine if the function attains its maximum or minimum at the stationary points, which by the way are limited in the fact that they must both satisfy the gradient equations and the constraint.


What does the autosum function do?

it adds up all the entries in a row or column.


What is a cofactor of a determinant?

The cofactor is the signed minor of a determinant, used to evaluate the determinant. You take the minor of the element - call that element aij - and if i + j is even, the cofactor is the minor - otherwise, it's the opposite of the minor. Thus, take the matrix, remove the row and column the element is in, and if the sum of the row number and column number is even, then there's your cofactor; otherwise, it's the additive inverse. For example, the cofactor of a34 is the determinant of the same matrix with the 3rd row and 4th column removed, and then you take the opposite (additive inverse or negative), because 3 + 4 = 7 is odd.


Does every square matrix have a determinant?

Yes, every square matrix has a determinant. The determinant is a scalar value that can be computed from the elements of the matrix and provides important information about the matrix, such as whether it is invertible. For an ( n \times n ) matrix, the determinant can be calculated using various methods, including cofactor expansion or row reduction. However, the determinant may be zero, indicating that the matrix is singular and not invertible.