Q. 29PA Use 聽A=1鈭�243,聽B=-5243, and聽... [FREE SOLUTION]

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Chapter 4: Q. 29PA (page 172)

Use $A = [\begin{matrix} 1 & 鈭� 2 \\ 4 & 3 \end{matrix}]$ , $B = [\begin{matrix} - 5 & 2 \\ 4 & 3 \end{matrix}]$ , 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 CA+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.

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

Step 2. Determine the value of AC+BC

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

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

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

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

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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91影视

Use $A = [\begin{matrix} 1 & 鈭� 2 \\ 4 & 3 \end{matrix}]$ , $B = [\begin{matrix} - 5 & 2 \\ 4 & 3 \end{matrix}]$ , 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 CA+B

Step 2. Determine the value of AC+BC

Step 3. Make the conclusion

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91影视

Use A=1鈭�243,B=-5243, andC=512-4and scalar c=3to determine whether the equation is true for the given matrices.CA+B=AC+BC

Short Answer

Step by step solution

Step 1. Determine the value of CA+B

Step 2. 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

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

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