How Can I Calculate Determinant, Cofactors, Adjugate, and Inverse of a Matrix?

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To calculate the determinant, cofactor matrix, adjugate, and inverse of the given 2x2 matrix A, first find the determinant using the formula det(A) = ad - bc, where A = [a b; c d]. The cofactor matrix involves calculating the minors and applying signs based on their positions. The adjugate matrix is the transpose of the cofactor matrix. Finally, the inverse can be found using A^-1 = (1/det(A)) * adj(A). Understanding these concepts is essential for solving the problem effectively.
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Homework Statement



Let A =

[ 3 2 ]
[ 6 7 ]

Find the following:

(a) det (A) = __

(b) the matrix of cofactors C = (__, __) (__, __)

(c) adj (A) = (__, __) (__, __)

(d) A^-1 = (__,__) (__, __)

Homework Equations


I am just not to familiar with what cofactor means, and adj(A), A^-1, as well as det(A).
How can I find all that from one matrix?

The Attempt at a Solution



I put the matrix into RREF, but for the determinant don't I have to like multiply diagonally or something?

Thank YOU!
 
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these are really simple for a 2 by 2 matrix. You're given the matrix A, and they ask for you det(A), matrix cofactors, adj(A), and A^-1.

det(A) means the determinant of A.

adj(A) means the adjugate matrix of A.

A^-1 means the inverse of A.

I'll get you started on the determinant. The determinant of a 2 by 2 matrix [a b]/ [c d]


is ad-bc
 
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