Answer D. 4
To calculate matrix rank transform matrix to upper
triangular
form using elementary row operations.

A1 
A2 
A3 
A4 
1 
1 
4 
8 
7 
2 
0 
0 
3 
0 
3 
4 
2 
3 
1 
4 
3 
12 
24 
2 
Multiply the 1st row by 4. R1>R1×4

A1 
A2 
A3 
A4 
1 
4 
16 
32 
28 
2 
0 
0 
3 
0 
3 
4 
2 
3 
1 
4 
3 
12 
24 
2 
Subtract the 1st row from the 3rd row and restore it R3>R3R1

A1 
A2 
A3 
A4 
1 
1 
4 
8 
7 
2 
0 
0 
3 
0 
3 
0 
14 
29 
27 
4 
3 
12 
24 
2 
Multiply the 1st row by 3. R1>R1×3

A1 
A2 
A3 
A4 
1 
3 
12 
24 
21 
2 
0 
0 
3 
0 
3 
0 
14 
29 
27 
4 
3 
12 
24 
2 
Subtract the 1st row from the 4th row and restore it. R4>R4R1

A1 
A2 
A3 
A4 
1 
1 
4 
8 
7 
2 
0 
0 
3 
0 
3 
0 
14 
29 
27 
4 
0 
0 
0 
19 
Swap the 2nd and the 3rd rows R2<>R3

A1 
A2 
A3 
A4 
1 
1 
4 
8 
7 
2 
0 
14 
29 
27 
3 
0 
0 
3 
0 
4 
0 
0 
0 
19 
Calculate the number of linearly independent rows

A1 
A2 
A3 
A4 
1 
1 
4 
8 
7 
2 
0 
14 
29 
27 
3 
0 
0 
3 
0 
4 
0 
0 
0 
19
