If {a_1}x + {b_1}y + {c_1}z = 0, {a_2}x + {b_ | vedclass

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

Question

(D) The given system of equations is a homogeneous system of linear equations of the form $AX = 0$,where $A$ is the coefficient matrix and $X = [x, y,

Vedclass · Accepted Answer

Infinite solution

Vedclass · Answer

(D) The given system of equations is a homogeneous system of linear equations of the form $AX = 0$,where $A$ is the coefficient matrix and $X = [x, y, z]^T$.For a homogeneous system $AX = 0$,the nature of the solution depends on the determinant of the coefficient matrix,denoted by $|A|$.If $|A| 
eq 0$,the system has only the trivial solution $(x = 0, y = 0, z = 0)$.If $|A| = 0$,the system has infinitely many non-trivial solutions in addition to the trivial solution.Since the problem states that $\left| \begin{matrix} {a_1} & {b_1} & {c_1} \ {a_2} & {b_2} & {c_2} \ {a_3} & {b_3} & {c_3} \end{matrix} ight| = 0$,the determinant of the coefficient matrix is zero.Therefore,the system has infinitely many solutions.

If ${a_1}x + {b_1}y + {c_1}z = 0, {a_2}x + {b_2}y + {c_2}z = 0, {a_3}x + {b_3}y + {c_3}z = 0$ and $\left| \begin{matrix} {a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3} \end{matrix} \right| = 0$,then the given system has

Similar Questions

If the system of equations $2x + \lambda y + 3z = 5$,$3x + 2y - z = 7$,and $4x + 5y + \mu z = 9$ has infinitely many solutions,then $(\lambda^2 + \mu^2)$ is equal to:

If the augmented matrix corresponding to the system of equations $x+y-z=1$, $2x+4y-z=0$ and $3x+4y+5z=18$ is transformed to $\left[\begin{array}{cccc}1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32\end{array}\right]$, then $\sqrt{a+b+c}=$

Consider the system of equations
$\begin{cases} x+y+z = 0 \\ \alpha x+\beta y+\gamma z = 0 \\ \alpha^{2} x+\beta^{2} y+\gamma^{2} z = 0 \end{cases}$
Then the system of equations has

Examine the consistency of the system of equations: $x+y+z=1$,$2x+3y+2z=2$,and $ax+ay+2az=4$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module