Find the determinant of matrix A
Calculate the determinant of matrix A using ad-bc for 2x2 or cofactor expansion for 3x3: the result determines invertibility and enables Cramer's rule for solving linear systems.
Key Concepts
To find the determinant of a matrix, go to the MATRIX menu and arrow over to the MATH submenu. Select the det( function. Then, go back to the MATRIX NAMES menu to select the matrix you want, like [A]. Close the parenthesis and press ENTER to calculate the single value determinant.
Example 1: For matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, using det([A]) on the calculator results in $ 2$. Example 2: For matrix $A = \begin{bmatrix} 2 & 0 \\ 7 & 3 \end{bmatrix}$, using det([A]) on the calculator results in $ 6$.
The determinant is a special number that tells you important things about a matrix. Instead of a tedious manual calculation, your calculator can find it in seconds! You just wrap the det() function around your stored matrix name. The calculator instantly processes it and gives you that one magical number that represents the matrix's unique properties.
Common Questions
What is the formula for the determinant of a 2x2 matrix?
For matrix A=[[a,b],[c,d]], det(A)=ad-bc. Multiply the main diagonal entries and subtract the product of the off-diagonal entries. For example det([[3,2],[1,4]])=(3)(4)-(2)(1)=10.
What does a zero determinant tell you about the matrix?
A determinant of zero means the matrix is singular and has no inverse. For a system AX=B, a zero determinant means the system either has no solution or infinitely many solutions, not a unique solution.
How is the determinant used in Cramer's rule?
Cramer's rule solves a system by computing determinants. Each variable's value is a ratio: the denominator is det(A) and the numerator is det of the matrix with the constant column replacing that variable's coefficient column.