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

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 $c (A B)$

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

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

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

– Determine the value of A(cB)

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

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

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

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

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

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=[1−243],B=[−5243], and C=[512−4] 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

Geometry

Logic and Functions

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Decision Maths

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