Determinants and I verse quiz part 1
1. What is a determinant?
a) A number that represents the ratio of sides of a triangle
b) A number that represents the area of a parallelogram
c) A number that represents the distance between two points
Answer: b) A number that represents the area of a parallelogram
2. How is the determinant of a 2x2 matrix calculated?
a) Subtract the product of the two diagonal elements
b) Add the product of the two diagonal elements
c) Multiply the two diagonal elements and subtract the product of the two off-diagonal elements
Answer: c) Multiply the two diagonal elements and subtract the product of the two off-diagonal elements
3. Which of the following is true for a matrix with a determinant of zero?
a) The matrix has no inverse
b) The matrix has a unique inverse
c) The matrix can have multiple inverses
Answer: a) The matrix has no inverse
4. What is the formula for the determinant of a 3x3 matrix?
a) The sum of the products of the elements in each row
b) The sum of the products of the elements in each column
c) The sum of the products of the elements in each diagonal
Answer: b) The sum of the products of the elements in each column
5. What is the inverse of a matrix?
a) The transpose of the matrix
b) The reciprocal of the matrix
c) The matrix that when multiplied by the original matrix results in the identity matrix
Answer: c) The matrix that when multiplied by the original matrix results in the identity matrix