Category 1: 2x2 Determinants
What is the formula for the determinant of a 2x2 matrix?
[ a b ]
[ c d ]
What is ad - bc?
What does a determinant of 0 indicate about a 3×3 matrix?
What is the matrix is not invertible?
The determinant of a matrix is used in this formula-based method for solving linear systems.
What is Cramer’s Rule?
What are D, Dₓ, Dᵧ, and D𝓏 in a 3-variable system?
What are the determinants used to find x, y, and z?
This operation helps you find out whether a matrix has an inverse
What is calculating the determinant?
Evaluate the determinant of
[ 6 -2 ]
[ 5 1 ]
What is 16?
This is the shortcut name for the method of computing a 3×3 determinant using diagonals.
What is Sarrus’ Rule*?
*multiplying elements along diagonals and summing the products, subtracting the products of elements along the other diagonals.
This is the formula to find x using Cramer’s Rule.
What is x = Dx/D?
How many determinants must you evaluate when solving a 3×3 system with Cramer’s Rule?
What is four?
The shape a matrix must be in to have a determinant.
What is a square matrix?
Evaluate the determinant of
[ 2 -11 ]
[ 0 0 ]
What is 0?
Evaluate the determinant:
[ 2 3 1 ]
[ 0 1 4 ]
[ 5 -2 0 ]
What is 71?
What must be true for Cramer’s Rule to apply?
What is D ≠ 0?
Given Dₓ = 12, D = 4, what is x?
What is 3?
What notation is used to denote a determinant?
What are vertical bars |A|?
If a 2x2 matrix has an entire row of zeros, what is its determinant?
What is 0?
Evaluate the determinant:
[ 1 0 2 ]
[ 3 1 0 ]
[ 0 4 5 ]
What is 29?
Solve using Cramer’s Rule:
{ 2x + 3y = 7
{ 4x + 5y = 9
What is x = -4, y = 5?
If D = 0, what does that mean for the system?
What is no solution or infinitely many solutions?
A matrix with a zero determinant is called this kind of matrix.
What is singular matrix?
Switching two rows in a 2×2 matrix has this effect on the determinant.
What is it changes the sign of the determinant?
If the determinant is nonzero, what can you conclude about the matrix?
What is the matrix is invertible and has a unique solution?
Solve using Cramer’s Rule:
{ -x + 2y = 3
{ 5x - 4y = -7
What is x = 2/-6 or -1/3, y = -8/-6 or 4/3?
Solve: D = 8, Dₓ = 16, Dᵧ = -24, D𝓏 = 0
What is x = 2, y = -3, z = 0?
If D = 0, what can you say about the system?
What is it has no solution or infinitely many?