The system of linear equations lambda x + y + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The augmented matrix $[A|B]$ is given by $\begin{bmatrix} \lambda & 1 & 1 & 3 \ 1 & -1 & -2 & 6 \ -1 & 1 & 1 & \mu \end{bmatrix}$.Performing row

Vedclass · Accepted Answer

infinite number of solutions for $\lambda = -1$ and $\mu = 3$

Vedclass · Answer

(B) The augmented matrix $[A|B]$ is given by $\begin{bmatrix} \lambda & 1 & 1 & 3 \ 1 & -1 & -2 & 6 \ -1 & 1 & 1 & \mu \end{bmatrix}$.Performing row operations:$R_1 \leftrightarrow R_2$ gives $\begin{bmatrix} 1 & -1 & -2 & 6 \ \lambda & 1 & 1 & 3 \ -1 & 1 & 1 & \mu \end{bmatrix}$.$R_3 ightarrow R_3 + R_1$ gives $\begin{bmatrix} 1 & -1 & -2 & 6 \ \lambda & 1 & 1 & 3 \ 0 & 0 & -1 & \mu + 6 \end{bmatrix}$.$R_2 ightarrow R_2 - \lambda R_1$ gives $\begin{bmatrix} 1 & -1 & -2 & 6 \ 0 & 1+\lambda & 1+2\lambda & 3-6\lambda \ 0 & 0 & -1 & \mu + 6 \end{bmatrix}$.For infinite solutions, the rank of the matrix must be less than the number of variables $(3)$.If $\lambda = -1$, the second row becomes $[0, 0, -1, 9]$.The system becomes consistent with infinite solutions if the equations are dependent, which occurs when $\mu = 3$.

The system of linear equations $\lambda x + y + z = 3$, $x - y - 2z = 6$, and $-x + y + z = \mu$ has:

Similar Questions

The system of linear equations $x + y + z = 6$, $2x + 5y + az = 36$, and $x + 2y + 3z = b$ has:

If the system of linear equations $2x + y - z = 7$,$x - 3y + 2z = 1$,and $x + 4y + \delta z = k$,where $\delta, k \in R$,has infinitely many solutions,then $\delta + k$ is equal to

Let the system of equations: $2x + 3y + 5z = 9$,$7x + 3y - 2z = 8$,$12x + 3y - (4 + \lambda)z = 16 - \mu$ have infinitely many solutions. Then the radius of the circle centred at $(\lambda, \mu)$ and touching the line $4x = 3y$ is

Let $A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1 \end{bmatrix}$,$B = \begin{bmatrix} 6 \\ 11 \\ 0 \end{bmatrix}$ and $X = \begin{bmatrix} a \\ b \\ c \end{bmatrix}$. If $AX = B$,then the value of $2a + b + 2c$ is:

Let the system of linear equations $x+y+kz=2$; $2x+3y-z=1$; $3x+4y+2z=k$ have infinitely many solutions. Then the system $(k+1)x+(2k-1)y=7$; $(2k+1)x+(k+5)y=10$ has:

Vedclass Test Series

Exam Paper Generator

Online Exam Module