System of Linear Equations

IMPORTANT

System of Linear Equations: Overview

This topic covers concepts, such as System of Linear Equations, Consistent and Inconsistent System of Linear Equations, Inverse Matrix Method to Solve System of Linear Equations, Homogeneous System of Linear Equations, etc.

Important Questions on System of Linear Equations

EASY

IMPORTANT

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

If x⁴ - x³ + ax² + x + b is exactly divisible by x² - 3x + 2, then the value of a and b are respectively.

MEDIUM

IMPORTANT

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

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>System of Linear Equations> Q 3

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>System of Linear Equations> Q 4

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>System of Linear Equations> Q 5

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>System of Linear Equations> Q 6

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>System of Linear Equations> Q 7

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>System of Linear Equations> Q 8

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>System 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>System of Linear Equations> Q 10

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>System of Linear Equations> Q 11

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>System of Linear Equations> Q 12

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>System of Linear Equations> Q 13

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>System of Linear Equations> Q 14

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>System of Linear Equations> Q 15

Let $A X = B$ be a system of $3$ linear equations with $3$ -unknowns. Let $X_{1}$ and $X_{2}$ be its two distinct solutions. If the combination $a X_{1} + b X_{2}$ is a solution of $A X = B$ ; where $a, b$ are real numbers, then which one of the following is correct?

MEDIUM

IMPORTANT

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

If the system of equations
$2 x + y - z = 5$

$2 x - 5 y + λ z = μ$

$x + 2 y - 5 z = 7$
has infinitely many solutions, then $(λ + μ)^{2} + (λ - μ)^{2}$ is equal to

MEDIUM

IMPORTANT

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

If the system of linear equations
$7 x + 11 y + α z = 13$
$5 x + 4 y + 7 z = β$
$175 x + 194 y + 57 z = 361$
has infinitely many solutions, then $α + β + 2$ is equal to

MEDIUM

IMPORTANT

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

For the system of linear equations

$2 x + 4 y + 2 a z = b$

$x + 2 y + 3 z = 4$

$2 x + 5 y + 2 z = 8$

which of the following is $NOT$ correct?

MEDIUM

IMPORTANT

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

For the system of linear equations

$2 x - y + 3 z = 5$

$3 x + 2 y - z = 7$

$4 x + 5 y + α z = β$ ,

which of the following is NOT correct?

EASY

IMPORTANT

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

For the system of equations

$x + y + z = 6$

$x + 2 y + α z = 10$

$x + 3 y + 5 z = β$ , which one of the following is NOT true?

System of Linear Equations

System of Linear Equations: Overview

Important Questions on System of Linear Equations

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