Math Practice
Check the determinant, then swap, negate and divide. The later problems use the inverse to solve systems of equations.
Find the determinant of
Does
Its determinant is
The inverse of
The determinant is 1; negate the top-right entry 1 to get
For the same matrix
Negate the bottom-left entry 5 and divide by the determinant 1:
What is the bottom-right entry of the inverse of
A diagonal matrix inverts entry by entry:
What is the bottom-left entry of the inverse of
The determinant is
What is the top-left entry of the inverse of
Swap in the 6 and divide by the determinant 10:
For which value of
Set the determinant to zero:
Use the inverse of
Use an inverse matrix to solve
The inverse of
What is the top-left entry of the inverse of
The determinant is
Find the determinant of the 3×3 matrix
Expand along the top row:
Mathematics verification: Mathematical formulas, calculations, worked examples and solutions are reviewed for accuracy before publication. How we check our work
These problems follow the inverse of a matrix lesson. Find the determinant first: if it’s zero, stop.
Type single entries and determinants as numbers or fractions like 3/2. Type solutions as ordered pairs like (1, 2), and yes or no where asked.
Then the matrix is singular and has no inverse, and the matching system has no unique solution.