Chapter 4: Q29. (page 172)

Use $A = [\begin{matrix} 1 & - 2 \\ 4 & 3 \end{matrix}]$ , $B = [\begin{matrix} - 5 & 2 \\ 4 & 3 \end{matrix}]$ , and $C = [\begin{matrix} 5 & 1 \\ 2 & - 4 \end{matrix}]$ and scalar $c = 3$ to determine whether the equation is true for the given matrices.
$C (A + B) = A C + B C$

Short Answer

Expert verified

The provided equation is false.

Step by step solution

Step 1- Determine the value of C(A+B)

Substitute the provided matrices into $C (A + B)$

$C (A + B) = [\begin{matrix} 5 & 1 \\ 2 & - 4 \end{matrix}] ([\begin{matrix} 1 & - 2 \\ 4 & 3 \end{matrix}] + [\begin{matrix} - 5 & 2 \\ 4 & 3 \end{matrix}])$

First perform the addition after it multiply the resulting matrix with C.

$\begin{matrix} C (A + B) = [\begin{matrix} 5 & 1 \\ 2 & - 4 \end{matrix}] \cdot [\begin{matrix} - 4 & 0 \\ 8 & 6 \end{matrix}] \\ = [\begin{matrix} 1 & 1 \\ 10 & 2 \end{matrix}] \end{matrix}$

– Determine the value of AC+BC

Substitute the provided matrices into $A C + B C$

$A C + B C = [\begin{matrix} 1 & - 2 \\ 4 & 3 \end{matrix}] \cdot [\begin{matrix} 5 & 1 \\ 2 & - 4 \end{matrix}] + [\begin{matrix} - 5 & 2 \\ 4 & 3 \end{matrix}] \cdot [\begin{matrix} 5 & 1 \\ 2 & - 4 \end{matrix}]$

First perform the multiplication between the matrices after it perform addition betwee the resulting matrices.

$\begin{matrix} A C + B C = [\begin{matrix} 1 & 9 \\ 26 & - 8 \end{matrix}] + [\begin{matrix} - 21 & - 13 \\ 26 & - 8 \end{matrix}] \\ = [\begin{matrix} - 20 & - 4 \\ 52 & - 16 \end{matrix}] \end{matrix}$

Step 3- Make the conclusion

As both the sides are not resulting in same matrix which means that the provided equation is false.

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Use $A = [\begin{matrix} 1 & - 2 \\ 4 & 3 \end{matrix}]$ , $B = [\begin{matrix} - 5 & 2 \\ 4 & 3 \end{matrix}]$ , and $C = [\begin{matrix} 5 & 1 \\ 2 & - 4 \end{matrix}]$ and scalar $c = 3$ to determine whether the equation is true for the given matrices.
$C (A + B) = A C + B C$

Short Answer

Step by step solution

Step 1- Determine the value of C(A+B)

– Determine the value of AC+BC

Step 3- Make the conclusion

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UseA=[1−243], B=[−5243], and C=[512−4]and scalar c=3to determine whether the equation is true for the given matrices.C(A+B)=AC+BC

Short Answer

Step by step solution

Step 1- Determine the value of C(A+B)

– Determine the value of AC+BC

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

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Statistics

Study anywhere. Anytime. Across all devices.

Use $A = [\begin{matrix} 1 & - 2 \\ 4 & 3 \end{matrix}]$ , $B = [\begin{matrix} - 5 & 2 \\ 4 & 3 \end{matrix}]$ , and $C = [\begin{matrix} 5 & 1 \\ 2 & - 4 \end{matrix}]$ and scalar $c = 3$ to determine whether the equation is true for the given matrices.
$C (A + B) = A C + B C$