Question

Match the cofactors to their corresponding entries in the matrix.

Answer 1

Answer:

The co-factors and their values are shown in the table below.

Step-by-step explanation:

We are given the matrix, $\begin{bmatrix}3&7&1\\7&1&-3\\8&5&1\end{bmatrix}$.

It is required to match the co-factors with the corresponding values.

As, the co-factors are given by,

$A_{c_{ij}}$ = $(-1)^{i+j}(d)$, where the d= determinant of the matrix after removing the i- row and j- column.

So, we have,

1. $A_{c_{11}}$.

So, $A_{c_{11}}=(-1)^{1+1}(1\times 1-5\times (-3))$

i.e. $A_{c_{11}}=(-1)^{2}(1+15)=16$

2. $A_{c_{13}}$.

So, $A_{c_{13}}=(-1)^{1+3}(7\times 5-1\times 8)$

i.e. $A_{c_{13}}=(-1)^{4}(35-8)=27$

3. $A_{c_{21}}$.

So, $A_{c_{21}}=(-1)^{2+1}(7\times 1-5\times 1)$

i.e. $A_{c_{21}}=(-1)^{3}(7-5)=-2$

4. $A_{c_{22}}$.

So, $A_{c_{22}}=(-1)^{2+2}(3\times 1-8\times 1)$

i.e. $A_{c_{22}}=(-1)^{4}(3-8)=-5$

5. $A_{c_{31}}$.

So, $A_{c_{31}}=(-1)^{3+1}(7\times (-3)-1\times 1)$

i.e. $A_{c_{31}}=(-1)^{4}(-21-1)=-22$

Thus, we get,

Co-factor                 Value

$A_{c_{11}}$                              16

$A_{c_{13}}$                             27

$A_{c_{21}}$                             -2

$A_{c_{22}}$                            -5

$A_{c_{31}}$                           -22