Systems of Linear Equations

IMPORTANT

Systems of Linear Equations: Overview

This topic covers concepts, such as, System of Linear Equations, Solutions of System of Linear Equations, Cramer's Rule (Determinants Method) to Solve System of Linear Equations & Cramer's Rule: Consistency of a System of Linear Equations etc.

Important Questions on Systems of Linear Equations

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 1

Using matrices, solve the following system of equation :

$\begin{array}{l} x + 2 y + z = 7 \\ x + 3 z = 11 \\ 2 x - 3 y = 1 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 2

Using matrices, solve the following system of equations :

$\begin{array}{l} 4 x + 3 y + 2 z = 60 \\ x + 2 y + 3 z = 45 \\ 6 x + 2 y + 3 z = 70 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 3

Using matrices, solve the following system of equation :

$2 x - y + z = 2, 3 x - z = 2, x + 2 y = 3$

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 4

Using matrices, solve the following system of equation :

$\begin{array}{l} 2 x - y + z = 2 \\ 3 x - z = 2 \\ x + 2 y = 3 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 5

Using matrices, solve the following system of equations

$\begin{array}{l} 4 x - 5 y - 11 z = 12 \end{array}$

$x - 3 y + z = 1$

$2 x + 3 y - 7 z = 2$

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 6

Using matrices, the solution of the following system of the equations would be:

$\begin{array}{l} 2 x - y + z = 0 \\ x + y - z = 6 \\ 3 x - y - 4 z = 7 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 7

Using matrices, the solution of the following system of equations would be:

$\begin{array}{l} x + 2 y - 3 z = 6 \\ 3 x + 2 y - 2 z = 3 \\ 2 x - y + z = 2 \end{array}$

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 8

Using matrix method the solution of the following system of linear equations would be:

$\begin{array}{l} x + y - z = 1, 3 x + y - 2 z = 3, x - y - z = 1 \end{array}$

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 9

Using matrix method the solution of the following system of linear equations would be:

$\begin{array}{l} x + y - z = 1 \\ 3 x + y - 2 z = 3 \\ x - y - z = 1. \end{array}$

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 10

Using matrix method solving of the following system of linear equations would be :

$\begin{array}{l} x + 2 y + z = 7 \\ x + 3 z = 11 \\ 2 x - 3 y = 1 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 11

Using matrix method, the solution of the following system of linear equations would be :

$\begin{array}{l} x + y - z = 1 \\ x - y - z = - 1 \\ 3 x + y - 2 z = 3 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 12

Using matrices, What would be the value of $x, y, z$ for the given equations.

$\begin{array}{l} 3 x + 4 y + 7 z = 4 \\ 2 x - y + 3 z = - 3 \\ x + 2 y - 3 z = 8 \end{array}$

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 13

Using matrices, what would be the value of $x, y, z$ for the following system of equations :

$\begin{array}{l} x + 2 y + z = 7 \end{array}$

$x + 3 z = 11$

$2 x - 3 y = 1$

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 14

The values of $s$ and $t$ , for which the system of equations
$x_{1} + x_{2} + x_{3} = 5$

$x_{1} + 2 x_{2} + 3 x_{3} = 9$

$x_{1} + 3 x_{2} + s x_{3} = t$

has no solution, are

EASY

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 15

If for positive real numbers $a, b$ and $c,$ the system of linear equations $x = a (y + z), y = b (z + x), z = c (x + y)$ has non-trivial solutions, then $\frac{1}{1 + a} + \frac{1}{1 + b} + \frac{1}{1 + c}$ is equal to

MEDIUM

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 16

If the system of linear equations $x + 3 y + 7 z = 0, - x + 4 y + 7 z = 0$ and $(\sin 3 θ) x + (\cos 2 θ) y + 2 z = 0$ has a non-trivial solution, then the number of values of $θ$ lying in the interval $[0, π]$ is

EASY

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 17

The equations $λ x - y = 2, 2 x - 3 y = - λ$ and $3 x - 2 y = - 1$ are consistent for

EASY

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 18

The system of simultaneous equations $k x + 2 y - z = 1, (k - 1) y - 2 z = 2$ and $(k + 2) z = 3$ has a unique solution, if $k$ equals

EASY

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 19

The system of equations $x + 2 y + 3 z = 1,$ $2 x + y + 3 z = 2$ and $5 x + 5 y + 9 z = 5$ has

HARD

IMPORTANT

Mathematics>Matrices and Determinants>Systems of Linear Equations> Q 20

If the system of equations $2 x + 3 y - z = 0, x + k y - 2 z = 0$ and $2 x - y + z = 0$ has a non-trivial solution $(x, y, z),$ then $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$ is equal to

Systems of Linear Equations

Systems of Linear Equations: Overview

Important Questions on Systems of Linear Equations

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