Finite Math Examples

Find the Adjoint [[cos(45),sin(60)],[sin(60),cos(-45)]]
Step 1
Consider the corresponding sign chart.
Step 2
Use the sign chart and the given matrix to find the cofactor of each element.
Tap for more steps...
Step 2.1
Calculate the minor for element .
Tap for more steps...
Step 2.1.1
The minor for is the determinant with row and column deleted.
Step 2.1.2
Evaluate the determinant.
Tap for more steps...
Step 2.1.2.1
The determinant of a matrix is the element itself.
Step 2.1.2.2
Simplify the determinant.
Tap for more steps...
Step 2.1.2.2.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 2.1.2.2.2
The exact value of is .
Step 2.2
Calculate the minor for element .
Tap for more steps...
Step 2.2.1
The minor for is the determinant with row and column deleted.
Step 2.2.2
Evaluate the determinant.
Tap for more steps...
Step 2.2.2.1
The determinant of a matrix is the element itself.
Step 2.2.2.2
The exact value of is .
Step 2.3
Calculate the minor for element .
Tap for more steps...
Step 2.3.1
The minor for is the determinant with row and column deleted.
Step 2.3.2
Evaluate the determinant.
Tap for more steps...
Step 2.3.2.1
The determinant of a matrix is the element itself.
Step 2.3.2.2
The exact value of is .
Step 2.4
Calculate the minor for element .
Tap for more steps...
Step 2.4.1
The minor for is the determinant with row and column deleted.
Step 2.4.2
Evaluate the determinant.
Tap for more steps...
Step 2.4.2.1
The determinant of a matrix is the element itself.
Step 2.4.2.2
The exact value of is .
Step 2.5
The cofactor matrix is a matrix of the minors with the sign changed for the elements in the positions on the sign chart.
Step 3
Transpose the matrix by switching its rows to columns.