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WorksheetsDeterminant of a 3x3 Matrix
Total questions: 10
Worksheet time: 5mins
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
