12/4 bell-ringer

Front

What is a determinant in a matrix?

Back

A determinant is a scalar value that is a function of the entries of a square matrix. It provides important information about the matrix, such as whether it is invertible.

Front

How do you calculate the determinant of a 2x2 matrix?

Back

For a 2x2 matrix A = ⌈a b⌉
⌊c d⌋, the determinant is calculated as det(A) = ad - bc.

Front

What is the determinant of the matrix ⌈12 -3⌉
⌊-6 15⌋?

Back

The determinant is 162.

Front

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

Back

If the determinant of a matrix is zero, it means that the matrix is singular and does not have an inverse.

Front

Calculate the determinant of the matrix ⌈1 2⌉
⌊3 4⌋.

Back

The determinant is (1*4) - (2*3) = 4 - 6 = -2.

Front

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

Back

For a 3x3 matrix A = ⌈a b c⌉
⌊d e f⌋
⌊g h i⌋, the determinant is calculated as det(A) = a(ei - fh) - b(di - fg) + c(dh - eg).

Front

Evaluate the determinant of the matrix ⌈5 6⌉
⌊7 8⌋.

Back

The determinant is (5*8) - (6*7) = 40 - 42 = -2.

Front

What is the significance of a non-zero determinant?

Back

A non-zero determinant indicates that the matrix is invertible and the system of equations it represents has a unique solution.

Front

How do you find the determinant of a matrix using row operations?

Back

Row operations can be used to simplify a matrix to upper triangular form, where the determinant is the product of the diagonal entries, adjusted for any row swaps.

Front

What is the determinant of the matrix ⌈2 3⌉
⌊4 5⌋?

Back

The determinant is (2*5) - (3*4) = 10 - 12 = -2.