A linear system of equations has n unknowns. The ranks of the coefficient matrix and the augmented matrix of the linear system of equations are $\mathbf{r}_{1}$ and $\mathbf{r}_{2}$, respectively. The condition for the equations to be consistent with a unique solution is

(A) $\mathbf{r}_{1}$ > $\mathbf{r}_{2}$

(B) $\mathrm{r}_{1}=\mathrm{r}_{2}=\mathrm{n}$

(C) $\mathbf{r}_{1}$=$\mathbf{r}_{2}$

(D) $r_{1} \neq r_{2}>n$

A linear system of equations has n unknowns. The ranks of the coefficient matrix and the augmented matrix of the linear system of equations are $\mathbf{r}_{1}$ and $\mathbf{r}_{2}$, respectively. The condition for the equations to be consistent with a unique solution is

(A) $\mathbf{r}_{1}$ > $\mathbf{r}_{2}$

(B) $\mathrm{r}_{1}=\mathrm{r}_{2}=\mathrm{n}$

(C) $\mathbf{r}_{1}$=$\mathbf{r}_{2}$

(D) $r_{1} \neq r_{2}>n$

1 Answer

127 votes

(B) $\mathrm{r}_{1}=\mathrm{r}_{2}=\mathrm{n}$

127 votes

127