If 𝐀=[ 2 3 1 9 1 0 5 0 6 7 8 4 ] 𝐁=[ 1

Name: Problem 10, Chapter 7: Mathematics for Economics and Business
Uploaded: 2022-01-31T19:31:20-08:00
Duration: 3 min 32 s
Channel: Niamat Khuda
Description: If 𝐀=[ 2 3 1 9 1 0 5 0 6 7 8 4 ] 𝐁=[ 1 7 9 6 2 1 0 5 6 4 5 3 ] work out (a) 2 𝐀 (b) 2 𝐁 (c) 2 A+2 𝐁 (d) 2(𝐀+𝐁) Do you notice any connection between your answers to parts (c) and (d)?

step 1 Hey guys, let's do problem 10. In this problem, matrix A and B are given. We need to find out tw

Question

If $$ \mathbf{A}=\left[\begin{array}{llll} 2 & 3 & 1 & 9 \\ 1 & 0 & 5 & 0 \\ 6 & 7 & 8 & 4 \end{array}\right] \quad \mathbf{B}=\left[\begin{array}{llll} 1 & 7 & 9 & 6 \\ 2 & 1 & 0 & 5 \\ 6 & 4 & 5 & 3 \end{array}\right] $$ work out (a) $2 \mathbf{A}$ (b) $2 \mathbf{B}$ (c) $2 \mathrm{~A}+2 \mathbf{B}$ (d) $2(\mathbf{A}+\mathbf{B})$ Do you notice any connection between your answers to parts (c) and (d)?

    If
$$
\mathbf{A}=\left[\begin{array}{llll}
2 & 3 & 1 & 9 \\
1 & 0 & 5 & 0 \\
6 & 7 & 8 & 4
\end{array}\right] \quad \mathbf{B}=\left[\begin{array}{llll}
1 & 7 & 9 & 6 \\
2 & 1 & 0 & 5 \\
6 & 4 & 5 & 3
\end{array}\right]
$$
work out
(a) $2 \mathbf{A}$
(b) $2 \mathbf{B}$
(c) $2 \mathrm{~A}+2 \mathbf{B}$
(d) $2(\mathbf{A}+\mathbf{B})$
Do you notice any connection between your answers to parts (c) and (d)?

Mathematics for Economics and Business

lan Jacques 5th Edition

Chapter 7, Problem 10

Instant Answer

Solved by Expert Niamat Khuda

01/31/2022

Step 1

We can do this by multiplying each element of $\mathbf{A}$ and $\mathbf{B}$ by 2. For $\mathbf{A}$, we get: $$ 2\mathbf{A}=\left[\begin{array}{llll} 2*2 & 2*3 & 2*1 & 2*9 \\ 2*1 & 2*0 & 2*5 & 2*0 \\ 2*6 & 2*7 & 2*8 & 2*4 \end{array}\right] = Show more…

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If $$ \mathbf{A}=\left[\begin{array}{llll} 2 & 3 & 1 & 9 \\ 1 & 0 & 5 & 0 \\ 6 & 7 & 8 & 4 \end{array}\right] \quad \mathbf{B}=\left[\begin{array}{llll} 1 & 7 & 9 & 6 \\ 2 & 1 & 0 & 5 \\ 6 & 4 & 5 & 3 \end{array}\right] $$ work out (a) $2 \mathbf{A}$ (b) $2 \mathbf{B}$ (c) $2 \mathrm{~A}+2 \mathbf{B}$ (d) $2(\mathbf{A}+\mathbf{B})$ Do you notice any connection between your answers to parts (c) and (d)?

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Key Concepts

Matrix Addition

Matrix addition involves combining two matrices of the same dimensions by adding their corresponding entries. It is a basic operation in linear algebra used to construct new matrices from existing ones.

Distributive Property

The distributive property in the context of matrices shows that a scalar multiplied by a sum of matrices equals the sum of each matrix multiplied by the scalar. This property confirms that 2(A + B) is equivalent to 2A + 2B, ensuring consistency in scalar and matrix operations.

Scalar Multiplication

Scalar multiplication is the process of multiplying every entry of a matrix by a constant factor. This operation scales the matrix and is fundamental in modifying matrices in various algebraic procedures.

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