Question

Find the cofactors of the elements 2 , -5 in the matrix (-1 o 5 . 1 2 -2
-4 -5 3

Answer 1

Answer:

The correct answers to this question are:

cofactor of 2 = 17

cofactor of -5 = 3

Step-by-step explanation:

Co-factor:

• The number we get when we remove the column and row of a selected element in a matrix is co-factor
• which is simply a numbers grid in the form of a rectangle or a square.
• The cofactor is always a positive or a negative value.

Given,

matrix =

             $\left[\begin{array}{ccc}-1&0&5\\1&2&-2\\-4&-5&3\end{array}\right]$

To find a co-factor

1. we need to remove the row and column of the respective element
2. find the determinant of the formed matrix
3. multiply with the respective sign $(-1)^{ij}$, where i,j are rows and columns

Co-factor of 2:

matrix formed =     $\left[\begin{array}{cc}-1&5\\-4&3\end{array}\right]$

determinant = (-1) * 3 - 5*(-4)

                    = -3 - (-20)

                    = -3 + 20

                    = 17

cofactor of 2 = 17 * $(-1)^{ij}$

= 17 * $(-1)^{22}$

= 17 * (-1)⁴

= 17 * 1

cofactor of 2 = 17

Co-factor of -5:

matrix formed =     $\left[\begin{array}{cc}-1&5\\1&-2\end{array}\right]$

determinant = (-1) * (-2) - 5*(1)

                    = 2 - 5

                    = -3

cofactor of -5 = (-3) * $(-1)^{ij}$

= (-3) * $(-1)^{32}$

= (-3) * (-1)⁵

= (-3) * (-1)

cofactor of -5 = 3

Hence, the final answer is

cofactor of 2 = 17

cofactor of -5 = 3

Click here for more about the matrix:

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Click here for more about the cofactor of a matrix:

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