Determinant of a 3x3 Matrix

What is the formula to calculate the determinant of a 3x3 matrix?

• det(A) = a(ei + fh) - b(di - fg) + c(dh - eg)

• det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)

• det(A) = a(ei - fh) + b(di + fg) - c(dh - eg)

• det(A) = a(ei - fh) - b(di - fg) - c(dh - eg)

Calculate the determinant of the matrix: [[2, 3, 1], [4, 5, 2], [1, 0, 3]]

• 2

• 7

• 10

• 5

What is the value of the determinant of a matrix if it is singular?

• 0

• 3

• 1

• 2

Find the determinant of the matrix: [[-1, 2, 3], [0, 4, -2], [1, 3, 5]]

• -42

• 7

• 10

• -12

What is the property of determinants when two rows of a matrix are identical?

• Determinant is negative

• Determinant is 1

• Determinant is 0

• Determinant is undefined

Calculate the determinant of the matrix: [[3, 1, 2], [0, -2, 1], [4, 3, 5]]

• -57

• 12

• 7

• -45

What is the significance of the determinant of a matrix in terms of its invertibility?

• The determinant being positive guarantees invertibility.

• The determinant being zero guarantees invertibility.

• The determinant of a matrix being non-zero indicates its invertibility.

• The determinant being negative guarantees invertibility.

Find the determinant of the matrix: [[-2, 1, 3], [4, 0, -1], [2, 3, 5]]

• -5

• 77

• 0

• 12

How does the determinant of a matrix change when its rows are interchanged?

• The determinant of a matrix changes sign when its rows are interchanged.

• The determinant of a matrix doubles when its rows are interchanged.

• The determinant of a matrix becomes zero when its rows are interchanged.

• The determinant of a matrix remains the same when its rows are interchanged.

Calculate the determinant of the matrix: [[1, 2, 3], [0, 1, 4], [2, 3, 5]]

• -20

• -25

• 7

• 10