Question:
The matrix equation \(AX=0\), represents :
A. non-Homogeneous linear equations
B. Homogeneous linear equations
C. Homogeneous non-linear equations
D. non-Homogeneous non-linear equations
E. non-Homogeneous Quadratic Equation
Choose the correct answer from the options given below :
The matrix equation \(AX=0\), represents :
A. non-Homogeneous linear equations
B. Homogeneous linear equations
C. Homogeneous non-linear equations
D. non-Homogeneous non-linear equations
E. non-Homogeneous Quadratic Equation Choose the correct answer from the options given below :
A. non-Homogeneous linear equations
B. Homogeneous linear equations
C. Homogeneous non-linear equations
D. non-Homogeneous non-linear equations
E. non-Homogeneous Quadratic Equation Choose the correct answer from the options given below :
Show Hint
Whenever the matrix equation is of the form
\[
AX=0
\]
the system is always homogeneous because the constants on the right side are zero.
Updated On: May 22, 2026
- A only
- B only
- C and D only
- D and E only
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
A system of equations written in matrix form is generally expressed as:
\[
AX=B
\]
where:
• \(A\) is the coefficient matrix,
• \(X\) is the variable matrix,
• \(B\) is the constant matrix. If: \[ B=0 \] then the system is called a homogeneous system. If: \[ B\neq0 \] then the system becomes non-homogeneous.
Step 1: Examining the given equation. The given equation is: \[ AX=0 \] The right-hand side is zero. Therefore the system is homogeneous.
Step 2: Checking whether the equation is linear or non-linear. In the equation: \[ AX=0 \] all variables occur only to the first degree. There are:
• no squares,
• no cubes,
• no products of variables,
• no trigonometric or exponential terms. Hence the equation is linear.
Step 3: Combining both observations. Thus: \[ AX=0 \] represents: \[ \boxed{\text{Homogeneous linear equations}} \]
Step 4: Verifying each option carefully.
• \(A\): non-homogeneous linear equations \(\rightarrow\) Incorrect
• \(B\): homogeneous linear equations \(\rightarrow\) Correct
• \(C\): homogeneous non-linear equations \(\rightarrow\) Incorrect
• \(D\): non-homogeneous non-linear equations \(\rightarrow\) Incorrect
• \(E\): non-homogeneous quadratic equation \(\rightarrow\) Incorrect Hence the correct answer is: \[ \boxed{(2)\; B\text{ only}} \]
• \(A\) is the coefficient matrix,
• \(X\) is the variable matrix,
• \(B\) is the constant matrix. If: \[ B=0 \] then the system is called a homogeneous system. If: \[ B\neq0 \] then the system becomes non-homogeneous.
Step 1: Examining the given equation. The given equation is: \[ AX=0 \] The right-hand side is zero. Therefore the system is homogeneous.
Step 2: Checking whether the equation is linear or non-linear. In the equation: \[ AX=0 \] all variables occur only to the first degree. There are:
• no squares,
• no cubes,
• no products of variables,
• no trigonometric or exponential terms. Hence the equation is linear.
Step 3: Combining both observations. Thus: \[ AX=0 \] represents: \[ \boxed{\text{Homogeneous linear equations}} \]
Step 4: Verifying each option carefully.
• \(A\): non-homogeneous linear equations \(\rightarrow\) Incorrect
• \(B\): homogeneous linear equations \(\rightarrow\) Correct
• \(C\): homogeneous non-linear equations \(\rightarrow\) Incorrect
• \(D\): non-homogeneous non-linear equations \(\rightarrow\) Incorrect
• \(E\): non-homogeneous quadratic equation \(\rightarrow\) Incorrect Hence the correct answer is: \[ \boxed{(2)\; B\text{ only}} \]
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