Q30. Use聽A=1鈭�243聽,B=鈭�5243聽, an... [FREE SOLUTION]

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Chapter 4: Q30. (page 172)

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

Short Answer

Expert verified

The provided equation is false.

Step by step solution

Step 1- Determine the value of ABC

Substitute the provided matrices into ABC.

$A B C = [\begin{matrix} 1 & 鈭� 2 \\ 4 & 3 \end{matrix}] 鈰� [\begin{matrix} 鈭� 5 & 2 \\ 4 & 3 \end{matrix}] 鈰� [\begin{matrix} 5 & 1 \\ 2 & 鈭� 4 \end{matrix}]$

First perform the multiplication between the matrices A and B after it multiply the resulting matrix with C.

$\begin{matrix} A B C = [\begin{matrix} 鈭� 13 & 鈭� 4 \\ 鈭� 8 & 17 \end{matrix}] 鈰� [\begin{matrix} 5 & 1 \\ 2 & 鈭� 4 \end{matrix}] \\ = [\begin{matrix} 鈭� 73 & 3 \\ 鈭� 6 & 鈭� 76 \end{matrix}] \end{matrix}$

– Determine the value of CBA

Substitute the provided matrices into CBA.

$C B A = [\begin{matrix} 5 & 1 \\ 2 & 鈭� 4 \end{matrix}] 鈰� [\begin{matrix} 鈭� 5 & 2 \\ 4 & 3 \end{matrix}] 鈰� [\begin{matrix} 1 & 鈭� 2 \\ 4 & 3 \end{matrix}]$

First perform the multiplication between the matrices C and B after it multiply the resulting matrix with A.

$\begin{matrix} C B A = [\begin{matrix} 鈭� 21 & 13 \\ 鈭� 26 & 鈭� 8 \end{matrix}] 鈰� [\begin{matrix} 1 & 鈭� 2 \\ 4 & 3 \end{matrix}] \\ = [\begin{matrix} 31 & 81 \\ 鈭� 58 & 28 \end{matrix}] \end{matrix}$

Step 3- Make the conclusion

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

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91影视

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

Short Answer

Step by step solution

Step 1- Determine the value of ABC

– Determine the value of CBA

Step 3- Make the conclusion

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91影视

UseA=1鈭�243,B=鈭�5243, and C=512鈭�4and scalar c=3to determine whether the equation is true for the given matrices.ABC=CBA

Short Answer

Step by step solution

Step 1- Determine the value of ABC

– Determine the value of CBA

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Pure Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

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