Find DA. Graph and describe the transformation. Transcription for Educational Website:---**Matrix Multiplication and Transformation**Given the matrices:\[ A = \begin{bmatrix} 2 & 4 & 3 & 5 \\ 3 & 6 & 6 & 8 \end{bmatrix} \]\[ D = \begin{bmatrix} 2 & 0 \\ 0 & 1.5 \end{bmatrix} \]**Task:**Find the product $ DA $ and graph the transformation.**Explanation:**To find the product matrix $ DA $, you multiply matrix $ D $ by matrix $ A $. Since $ D $ is a 2x2 matrix and $ A $ is a 2x4 matrix, the result $ DA $ will be a 2x4 matrix. Each element in the resulting matrix is calculated as the dot product of the corresponding row of $ D $ and column of $ A $.**Description:**Multiplying matrix $ A $ by matrix $ D $ scales the vectors represented by the columns of $ A $. Each column vector in $ A $ is transformed by the scaling factors from matrix $ D $, which in this case are 2 in the x-direction and 1.5 in the y-direction. This transformation stretches and compresses the original matrix $ A $.Graphically represent the transformation to visualize how the points are scaled by the factors from matrix $ D $.---

GIven matrix are A=24353668 D=2001.5 To find DA : As D is a 2*2 matrix and A is 2*4 matrix,…

Answered: [2 A- D- 4 3 51 [3 6 6 81 1.5 Find DA.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find DA. Graph and describe the transformation.

Transcription for Educational Website:

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**Matrix Multiplication and Transformation**

Given the matrices:

\[
A = \begin{bmatrix}
2 & 4 & 3 & 5 \\
3 & 6 & 6 & 8
\end{bmatrix}
\]

\[
D = \begin{bmatrix}
2 & 0 \\
0 & 1.5
\end{bmatrix}
\]

**Task:**

Find the product $ DA $ and graph the transformation.

**Explanation:**

To find the product matrix $ DA $, you multiply matrix $ D $ by matrix $ A $. Since $ D $ is a 2x2 matrix and $ A $ is a 2x4 matrix, the result $ DA $ will be a 2x4 matrix. Each element in the resulting matrix is calculated as the dot product of the corresponding row of $ D $ and column of $ A $.

**Description:**

Multiplying matrix $ A $ by matrix $ D $ scales the vectors represented by the columns of $ A $. Each column vector in $ A $ is transformed by the scaling factors from matrix $ D $, which in this case are 2 in the x-direction and 1.5 in the y-direction. This transformation stretches and compresses the original matrix $ A $.

Graphically represent the transformation to visualize how the points are scaled by the factors from matrix $ D $.

---

Expert Solution

Step 1

GIven matrix are

$A = [\begin{matrix} 2 & 4 & 3 & 5 \\ 3 & 6 & 6 & 8 \end{matrix}]$

$D = [\begin{matrix} 2 & 0 \\ 0 & 1.5 \end{matrix}]$

To find DA :

As D is a 2*2 matrix and A is 2*4 matrix, therefore DA multiplication holds and it will give a 2*4 matrix.

$D A = [\begin{matrix} 2 & 0 \\ 0 & 1.5 \end{matrix}] [\begin{matrix} 2 & 3 & 4 & 5 \\ 3 & 6 & 6 & 8 \end{matrix}] = [\begin{matrix} 4 & 6 & 8 & 10 \\ 4.5 & 9 & 9 & 12 \end{matrix}]$

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