Consider the simultaneous linear equations be | vedclass

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

Question

(B) Given the system of linear equations:$1) \beta x + \alpha y - z = -1$$2) 3x - \beta y + \alpha z = 0$$3) \alpha x + \beta y + z = 1$Using Cramer's

Vedclass · Accepted Answer

$(2, 1)$

Vedclass · Answer

(B) Given the system of linear equations:$1) \beta x + \alpha y - z = -1$$2) 3x - \beta y + \alpha z = 0$$3) \alpha x + \beta y + z = 1$Using Cramer's rule, the solutions are $x = \frac{\Delta_1}{\Delta} = -1$, $y = \frac{\Delta_2}{\Delta} = 1$, and $z = \frac{\Delta_3}{\Delta} = 2$.Substitute these values into the equations:From $(1)$: $\beta(-1) + \alpha(1) - 2 = -1 \Rightarrow \alpha - \beta = 1$From $(2)$: $3(-1) - \beta(1) + \alpha(2) = 0 \Rightarrow 2\alpha - \beta = 3$From $(3)$: $\alpha(-1) + \beta(1) + 2 = 1 \Rightarrow -\alpha + \beta = -1 \Rightarrow \alpha - \beta = 1$Now solve the system of equations for $\alpha$ and $\beta$:$\alpha - \beta = 1$$2\alpha - \beta = 3$Subtract the first equation from the second:$(2\alpha - \beta) - (\alpha - \beta) = 3 - 1$$\alpha = 2$Substitute $\alpha = 2$ into $\alpha - \beta = 1$:$2 - \beta = 1 \Rightarrow \beta = 1$Thus, $(\alpha, \beta) = (2, 1)$.

Similar Questions

Let $[\lambda]$ be the greatest integer less than or equal to $\lambda$. The set of all values of $\lambda$ for which the system of linear equations $x+y+z=4$,$3x+2y+5z=3$,$9x+4y+(28+[\lambda])z=[\lambda]$ has a solution is:

If the system of linear equations $x - 4y + 7z = g$,$3y - 5z = h$,and $-2x + 5y - 9z = k$ is consistent,then:

Let $AX=D$ be a system of three linear non-homogeneous equations. If $|A|=0$ and $\operatorname{rank}(A)=\operatorname{rank}([AD])=\alpha$, then

If the system of equations $x+y+2z=3$, $x+2y+3z=4$ and $x+y+cz=5$ is inconsistent, then:

The number of solutions of the following equations $x_2 - x_3 = 1$,$-x_1 + 2x_3 = -2$,$x_1 - 2x_2 = 3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module