If verify that
A (B + C) = (AB + AC).
$\mathrm{A}=\left[\begin{array}{ll}2 & 1\end{array}\right], \quad \mathrm{B}=\left[\begin{array}{lll}5 & 3 & 4 \\ 8 & 7 & 6\end{array}\right]$ and $\mathrm{C}=\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 0 & 2\end{array}\right]$
Given, $A=\left[\begin{array}{ll}2 & 1\end{array}\right], B=\left[\begin{array}{lll}5 & 3 & 4 \\ 8 & 7 & 6\end{array}\right]$ and $C=\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 0 & 2\end{array}\right]$
Now,
$A(B+C)=\left[\begin{array}{ll}2 & 1\end{array}\right]\left[\begin{array}{lll}5-1 & 3+2 & 4+1 \\ 8+1 & 7+0 & 6+2\end{array}\right]$
$=\left[\begin{array}{ll}2 & 1\end{array}\right]\left[\begin{array}{lll}4 & 5 & 5 \\ 9 & 7 & 8\end{array}\right]$
$=[8+910+710+8]$
$=\left[\begin{array}{lll}17 & 17 & 18\end{array}\right]$ ...(i)
And,
$A B=\left[\begin{array}{ll}2 & 1\end{array}\right]\left[\begin{array}{lll}5 & 3 & 4 \\ 8 & 7 & 6\end{array}\right]=[10+86+78+6]=\left[\begin{array}{lll}18 & 13 & 14\end{array}\right]$
And,
$A C=\left[\begin{array}{ll}2 & 1\end{array}\right]\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 0 & 2\end{array}\right]=[-2+14+02+2]=\left[\begin{array}{lll}-1 & 4 & 4\end{array}\right]$
So, $A B+A C=\left[\begin{array}{llll}18 & 13 & 14\end{array}\right]+\left[\begin{array}{lll}-1 & 4 & 4\end{array}\right]$
$=\left[\begin{array}{lll}17 & 17 & 18\end{array}\right]$ $\ldots$ (ii)
From equations (i) and (ii),
$A(B+C)=(A B+A C)$
Hence, verified
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All Study Material
- 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
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,