Chapter 4: Q3. (page 171)

Explain why, in most cases $(A + B) C \neq C A + C B$

Short Answer

Expert verified

The distributive property is not always true for matrices.

Step by step solution

Step 1- Observe the provided information

The provided information indicates towards distributive property.

– Use the observation

Solving matrix by distributive property $a (b + c) = a b + a c$ will lead to different matrix on both the sides most of the times.

For example,

Considerlocalid="1648734720106" $A = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ localid="1648734733768" $B = [\begin{matrix} 2 & 2 \\ 1 & 2 \end{matrix}]$ and localid="1648734748052" $C = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$

Determine the value of $(A + B) C$

localid="1648734790943" $\begin{matrix} (A + B) C = [\begin{matrix} 3 & 4 \\ 3 & 3 \end{matrix}] \cdot [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] \\ = [\begin{matrix} 4 & 3 \\ 3 & 3 \end{matrix}] \end{matrix}$

Determine the value of $C A + C B$

localid="1648735012033" $\begin{matrix} C A + C B = [\begin{matrix} 2 & 1 \\ 1 & 2 \end{matrix}] + [\begin{matrix} 1 & 2 \\ 2 & 2 \end{matrix}] \\ = [\begin{matrix} 3 & 3 \\ 3 & 4 \end{matrix}] \end{matrix}$

Both the matrices are not the same.

Step 3- Write the conclusion

The using of observation results in that the distributive property is not always true for the matrices.

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Explain why, in most cases $(A + B) C \neq C A + C B$

Short Answer

Step by step solution

Step 1- Observe the provided information

– Use the observation

Step 3- Write the conclusion

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Explain why, in most cases(A+B)C≠CA+CB

Short Answer

Step by step solution

Step 1- Observe the provided information

– Use the observation

Step 3- Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Applied Mathematics

Geometry

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Explain why, in most cases $(A + B) C \neq C A + C B$