The rank of the matrix A=[2 3 1 4 0 1 2 -1 0 -2 -4 2] is

Question

The rank of the matrix A=[2 3 1 4 0 1 2 -1 0 -2 -4 2] is (A) 2 (B) 3 (C) 1 (D) indeterminate

Tardigrade Admin · Accepted Answer

Given A=[2 3 1 4 0 1 2 -1 0 -2 -4 2] Rank of A ≤ min 3,4 So, rank of A ≤ 3 Now, we will reduce it to Echelon form R 3 arrow R 3+2 R 2 [2 3 1 4 0 1 2 -1 0 0 0 0] Here, row R3 has all elements 0 . So, two non-zero rows. Hence, rank=2

Q. The rank of the matrix $A = ⎣ ⎡ 200 31 - 2 12 - 4 4 - 1 2 ⎦ ⎤$ is

2

3

1

indeterminate

Given $A = ⎣ ⎡ 200 31 - 2 12 - 4 4 - 1 2 ⎦ ⎤$
Rank of $A \leq min 3, 4$
So, rank of $A \leq 3$
Now, we will reduce it to Echelon form
$R_{3} \to R_{3} + 2 R_{2}$
$⎣ ⎡ 200310120 4 - 1 0 ⎦ ⎤$
Here, row $R_{3}$ has all elements $0$ .
So, two non-zero rows.
Hence, rank $= 2$

Q. The rank of the matrix A=⎣⎡​200​31−2​12−4​4−12​⎦⎤​ is

2

3

1

indeterminate

Given A=⎣⎡​200​31−2​12−4​4−12​⎦⎤​ Rank of A≤min3,4 So, rank of A≤3 Now, we will reduce it to Echelon form R3​→R3​+2R2​ ⎣⎡​200​310​120​4−10​⎦⎤​ Here, row R3​ has all elements 0 . So, two non-zero rows. Hence, rank=2

Q. The rank of the matrix $A = ⎣ ⎡ 200 31 - 2 12 - 4 4 - 1 2 ⎦ ⎤$ is

Given $A = ⎣ ⎡ 200 31 - 2 12 - 4 4 - 1 2 ⎦ ⎤$
Rank of $A \leq min 3, 4$
So, rank of $A \leq 3$
Now, we will reduce it to Echelon form
$R_{3} \to R_{3} + 2 R_{2}$
$⎣ ⎡ 200310120 4 - 1 0 ⎦ ⎤$
Here, row $R_{3}$ has all elements $0$ .
So, two non-zero rows.
Hence, rank $= 2$