Q10P GivenA=(1236),聽C=(7623),聽D=(-3... [FREE SOLUTION]

Chapter 3: Q10P (page 122)

Given
$A = (\begin{matrix} 1 & 2 \\ 3 & 6 \end{matrix}), C = (\begin{matrix} 7 & 6 \\ 2 & 3 \end{matrix}), D = (\begin{matrix} - 3 & 2 \\ 7 & 5 \end{matrix})$
Show that, $AC = AD, but C 鈮� D AND A 鈮� 0$ .

Short Answer

Expert verified

Find the products AC and AD of the given matrices to prove that AC=AD, but $C 鈮� D and A 鈮� 0 .$ .

Step by step solution

Definition of Matrix multiplication:

The element in row iand column j of the product matrix ABis equal to row iof Atimes column j of B. In index notation ${(AB)}_{ij} = \underset{k}{鈭� A_{ik} B_{kj}}$ .

For example, if $A = (\begin{matrix} a & b \\ c & d \end{matrix}) and B = (\begin{matrix} e & f \\ c & d \end{matrix}) then, AB = (\begin{matrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{matrix})$ and then,

Multiply Matrices:

The give matrices are

$A = (\begin{matrix} 1 & 2 \\ 3 & 6 \end{matrix}), C = (\begin{matrix} 7 & 6 \\ 2 & 3 \end{matrix}) and D = (\begin{matrix} - 3 & 2 \\ 7 & 5 \end{matrix})$

It needs to be proved that $AC = AD, but C 鈮� D and, A 鈮� 0$

$AC = (\begin{matrix} 1 & 2 \\ 3 & 6 \end{matrix}) (\begin{matrix} 7 & 6 \\ 2 & 3 \end{matrix}) = (\begin{matrix} 7 + 4 & 6 + 6 \\ 21 + 12 & 18 + 18 \end{matrix}) = (\begin{matrix} 11 & 12 \\ 33 & 36 \end{matrix}) And AD = (\begin{matrix} 1 & 2 \\ 3 & 6 \end{matrix}) (\begin{matrix} - 3 & 2 \\ 7 & 5 \end{matrix}) = (\begin{matrix} - 3 + 14 & 2 + 10 \\ - 9 + 42 & 6 + 30 \end{matrix}) = (\begin{matrix} 11 & 12 \\ 33 & 36 \end{matrix})$

$Thus, AC = AD, while C 鈮� D and A 鈮� 0 .$

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91影视

Given
$A = (\begin{matrix} 1 & 2 \\ 3 & 6 \end{matrix}), C = (\begin{matrix} 7 & 6 \\ 2 & 3 \end{matrix}), D = (\begin{matrix} - 3 & 2 \\ 7 & 5 \end{matrix})$
Show that, $AC = AD, but C 鈮� D AND A 鈮� 0$ .

Short Answer

Step by step solution

Definition of Matrix multiplication:

Multiply Matrices:

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

GivenA=(1236),C=(7623),D=(-3275)Show that,AC=AD,butC鈮�DANDA鈮�0.

Short Answer

Step by step solution

Definition of Matrix multiplication:

Multiply Matrices:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Quantum Physics

Particle Model of Matter

Astrophysics

Atoms and Radioactivity

Nuclear Physics

Study anywhere. Anytime. Across all devices.

Given
$A = (\begin{matrix} 1 & 2 \\ 3 & 6 \end{matrix}), C = (\begin{matrix} 7 & 6 \\ 2 & 3 \end{matrix}), D = (\begin{matrix} - 3 & 2 \\ 7 & 5 \end{matrix})$
Show that, $AC = AD, but C 鈮� D AND A 鈮� 0$ .