Q10. UseA=[2鈭�135]聽,B=[鈭�4180] , a... [FREE SOLUTION]

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Chapter 4: Q10. (page 171)

Use $A = [\begin{matrix} 2 & 鈭� 1 \\ 3 & 5 \end{matrix}]$ , $B = [\begin{matrix} 鈭� 4 & 1 \\ 8 & 0 \end{matrix}]$ , and $C = [\begin{matrix} 3 & 2 \\ 鈭� 1 & 2 \end{matrix}]$ to determine whether $A (B C) = (A B) C$ is true for the given matrices.

Short Answer

Expert verified

Yes, the provided equation is true.

Step by step solution

Step 1- Determine the value of A(BC)

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

$A (B C) = [\begin{matrix} 2 & 鈭� 1 \\ 3 & 5 \end{matrix}] ([\begin{matrix} 鈭� 4 & 1 \\ 8 & 0 \end{matrix}] 鈰� [\begin{matrix} 3 & 2 \\ 鈭� 1 & 2 \end{matrix}])$

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

$\begin{matrix} A (B C) = [\begin{matrix} 2 & 鈭� 1 \\ 3 & 5 \end{matrix}] 鈰� [\begin{matrix} 鈭� 13 & 鈭� 6 \\ 24 & 16 \end{matrix}] \\ = [\begin{matrix} 鈭� 50 & 鈭� 28 \\ 81 & 62 \end{matrix}] \end{matrix}$

– Determine the value of (AB)C

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

$(A B) C = ([\begin{matrix} 2 & 鈭� 1 \\ 3 & 5 \end{matrix}] 鈰� [\begin{matrix} 鈭� 4 & 1 \\ 8 & 0 \end{matrix}]) [\begin{matrix} 3 & 2 \\ 鈭� 1 & 2 \end{matrix}]$

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

$\begin{matrix} (A B) C = [\begin{matrix} 鈭� 16 & 2 \\ 28 & 3 \end{matrix}] 鈰� [\begin{matrix} 3 & 2 \\ 鈭� 1 & 2 \end{matrix}] \\ = [\begin{matrix} 鈭� 50 & 鈭� 28 \\ 81 & 62 \end{matrix}] \end{matrix}$

Step 3- Make the conclusion

As both the sides results in same matrix which means that the provided equation is true.

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91影视

Use $A = [\begin{matrix} 2 & 鈭� 1 \\ 3 & 5 \end{matrix}]$ , $B = [\begin{matrix} 鈭� 4 & 1 \\ 8 & 0 \end{matrix}]$ , and $C = [\begin{matrix} 3 & 2 \\ 鈭� 1 & 2 \end{matrix}]$ to determine whether $A (B C) = (A B) C$ is true for the given matrices.

Short Answer

Step by step solution

Step 1- Determine the value of A(BC)

– Determine the value of (AB)C

Step 3- Make the conclusion

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91影视

UseA=[2鈭�135],B=[鈭�4180] , andC=[32鈭�12] to determine whetherA(BC)=(AB)C is true for the given matrices.

Short Answer

Step by step solution

Step 1- Determine the value of A(BC)

– Determine the value of (AB)C

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use $A = [\begin{matrix} 2 & 鈭� 1 \\ 3 & 5 \end{matrix}]$ , $B = [\begin{matrix} 鈭� 4 & 1 \\ 8 & 0 \end{matrix}]$ , and $C = [\begin{matrix} 3 & 2 \\ 鈭� 1 & 2 \end{matrix}]$ to determine whether $A (B C) = (A B) C$ is true for the given matrices.