Question:
If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$, then show that $|2 A|=4|A|$
Solution:
The given matrix is $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$.
$\therefore 2 A=2\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]=\left[\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right]$
$\therefore$ L.H.S. $=|2 A|=\left|\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right|=2 \times 4-4 \times 8=8-32=-24$
Now, $|A|=\left|\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right|=1 \times 2-2 \times 4=2-8=-6$
$\therefore$ R.H.S $=4|A|=4 \times(-6)=-24$
$\therefore$ L.H.S. $=$ R.H.S.
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
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- Atoms
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