Welcome to your Grade 11 Mathematics chapter 4
After carefully reading the following 30 questions, choose the correct answer.
1.
For a 2×2 matrix A=(acbd), how is the determinant det(A) calculated?
2.
What is the minor Mij of an element aij in a square matrix?
3.
The cofactor Cij of an element aij is defined by which formula?
4.
If all elements of a row in a square matrix are zero, what is the value of its determinant?
5.
What happens to the determinant of a matrix if two rows are interchanged?
6.
If two rows of a square matrix are identical, the determinant is:
7.
When a single row of matrix A is multiplied by a scalar k to form matrix B, how are their determinants related?
8.
Adding a multiple of one row to another row of a square matrix:
9.
The determinant of a triangular matrix is the:
10.
For any square matrix A, which of the following is true regarding its transpose AT?
11.
Cramer's Rule is used to solve a system of n linear equations in n variables provided that:
12.
In Cramer's Rule, the value of variable xi is found by:
13.
The adjoint of a matrix A, denoted adj(A), is the:
14.
The inverse of a square matrix A can be calculated using the adjoint as:
15.
For 3×3 matrices A and B, det(AB) is equal to:
16.
If det(A)=5 for a 2×2 matrix, what is det(2A)?
17.
A matrix A is singular if:
18.
Expansion by cofactors can be performed along:
19.
If a square matrix A has an inverse, then det(A−1) is:
20.
Sarrus' Rule is a mnemonic for computing the determinant of which order matrix?
21.
If the determinant of a coefficient matrix in a system of linear equations is zero, then the system:
22.
The determinant of the identity matrix In is always:
23.
In a 3×3 matrix, the sign pattern for cofactors follows which starting sign at C11?
24.
If A is a square matrix and det(A)=k, then det(A2) is:
25.
Which property is used when det(A) is evaluated by making the matrix upper triangular?
26.
If a matrix B is obtained by multiplying every element of an n×n matrix A by k, then det(B)=
27.
If det(A)=0, the system AX=B has how many solutions?
28.
The determinant of a diagonal matrix is:
29.
For a 2×2 matrix A, adj(A) is formed by interchanging the main diagonal elements and:
30.
Expansion of det(A) along the i-th row is given by the sum of aijCij for j=1 to n. This is known as:
31.
If the matrix A is skew-symmetric (AT=−A) and of odd order, its determinant is:
