Q28. UseA=[1鈭�243]聽,B=[鈭�5243]聽, ... [FREE SOLUTION]

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Chapter 4: Q28. (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.
$c (A B) = A (c B)$

Short Answer

Expert verified

Yes, the provided equation is true.

Step by step solution

Step 1- Determine the value of c(AB)

Substitute the provided matrices into $c (A B)$

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

First perform the multiplication between the matrices after it multiply the resulting matrix with c.

$\begin{matrix} c (A B) = 3 [\begin{matrix} 鈭� 13 & 鈭� 4 \\ 鈭� 8 & 17 \end{matrix}] \\ = [\begin{matrix} 鈭� 39 & 鈭� 12 \\ 鈭� 24 & 51 \end{matrix}] \end{matrix}$

– Determine the value of A(cB)

Substitute the provided matrices into $A (c B)$

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

First perform the multiplication between the matrix B and scalar c after it multiply the resulting matrix with A.

$\begin{matrix} A (c B) = [\begin{matrix} 1 & 鈭� 2 \\ 4 & 3 \end{matrix}] 鈰� [\begin{matrix} 鈭� 15 & 6 \\ 12 & 9 \end{matrix}] \\ = [\begin{matrix} 鈭� 39 & 鈭� 12 \\ 鈭� 24 & 51 \end{matrix}] \end{matrix}$

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

Short Answer

Step by step solution

Step 1- Determine the value of c(AB)

– Determine the value of A(cB)

Step 3- Make the conclusion

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UseA=[1鈭�243],B=[鈭�5243], and C=[512鈭�4] and scalar c=3to determine whether the equation is true for the given matrices.c(AB)=A(cB)

Short Answer

Step by step solution

Step 1- Determine the value of c(AB)

– Determine the value of A(cB)

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Discrete Mathematics

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.
$c (A B) = A (c B)$