Matrix Determinants and Inverses

Front

What is a matrix determinant?

Back

A scalar value that is a function of the entries of a square matrix, providing important properties such as whether the matrix is invertible.

Front

How do you determine if a matrix has an inverse?

Back

A matrix has an inverse if and only if its determinant is non-zero.

Front

What is the determinant of a 2x2 matrix |a b| |c d|?

Back

The determinant is calculated as ad - bc.

Front

What does it mean if the determinant of a matrix is 0?

Back

It means the matrix is singular and does not have an inverse.

Front

How do you find the inverse of a 2x2 matrix |a b| |c d|?

Back

The inverse is given by (1/det) * |d -b| |-c a|, where det = ad - bc.

Front

What is the formula for the determinant of a 3x3 matrix?

Back

For a matrix |a b c| |d e f| |g h i|, the determinant is a(ei - fh) - b(di - fg) + c(dh - eg).

Front

What is a multiplicative inverse?

Back

The multiplicative inverse of a number x is 1/x, such that x * (1/x) = 1.

Front

What is the relationship between a matrix and its inverse?

Back

If A is a matrix and A^-1 is its inverse, then A * A^-1 = I, where I is the identity matrix.

Front

What is an asymptote in relation to functions?

Back

An asymptote is a line that a graph approaches but never touches, indicating the behavior of the function at extreme values.

Front

What is the significance of a non-zero determinant in linear algebra?

Back

A non-zero determinant indicates that the matrix represents a unique solution to a system of linear equations.