Question

Let $$\mathbf{A}=\left[\begin{array}{rrr}3 & 0 & 4 \\-1 & 2 & 2 \\6 & 5 & -4\end{array}\right], \mathbf{B}=\left[\begin{array}{rrr}0 & -5 & -3 \\-5 & 2 & 4 \\-3 & 4 & 0\end{array}\right],$$ $$\mathbf{C}=\left[\begin{array}{ll}0 & 2 \\2 & 4 \\1 & 3\end{array}\right], \quad \mathbf{D}=\left[\begin{array}{rr}6 & 1 \\-4 & 7 \\-8 & 3\end{array}\right],$$ $$\mathbf{u}=\left[\begin{array}{r}2 \\0 \\-1\end{array}\right], \quad\mathbf{v}=\left[\begin{array}{r}-45 \\0.8 \\1.2\end{array}\right].$$ Find the following expressions or give reasons why they are undefined. $$\mathbf{A}+\mathbf{C}-\mathbf{D}, \mathbf{C}-\mathbf{D}, \mathbf{D}-\mathbf{C}, \mathbf{B}+2 \mathbf{C}+4 \mathbf{D}$$

Name: Problem 3, Chapter 7: Advanced Engineering Mathematics
Uploaded: 2021-12-25T07:55:32-08:00
Duration: 2 min 11 s
Channel: Saurabh Kumar Gupta
Description: Let 𝐀=[ 3 0 4 -1 2 2 6 5 -4 ], 𝐁=[ 0 -5 -3 -5 2 4 -3 4 0 ], 𝐂=[ 0 2 2 4 1 3 ], 𝐃=[ 6 1 -4 7 -8 3 ], 𝐮=[ 2 0 -1 ], 𝐯=[ -45 0.8 1.2 ]. Find the following expressions or give reasons why they are undefined. 𝐀+𝐂-𝐃, 𝐂-𝐃, 𝐃-𝐂, 𝐁+2 𝐂+4 𝐃

   Let $$\mathbf{A}=\left[\begin{array}{rrr}3 & 0 & 4 \\-1 & 2 & 2 \\6 & 5 & -4\end{array}\right], \mathbf{B}=\left[\begin{array}{rrr}0 & -5 & -3 \\-5 & 2 & 4 \\-3 & 4 & 0\end{array}\right],$$
$$\mathbf{C}=\left[\begin{array}{ll}0 & 2 \\2 & 4 \\1 & 3\end{array}\right], \quad \mathbf{D}=\left[\begin{array}{rr}6 & 1 \\-4 & 7 \\-8 & 3\end{array}\right],$$ $$\mathbf{u}=\left[\begin{array}{r}2 \\0 \\-1\end{array}\right], \quad\mathbf{v}=\left[\begin{array}{r}-45 \\0.8 \\1.2\end{array}\right].$$
Find the following expressions or give reasons why they are undefined.
$$\mathbf{A}+\mathbf{C}-\mathbf{D}, \mathbf{C}-\mathbf{D}, \mathbf{D}-\mathbf{C}, \mathbf{B}+2 \mathbf{C}+4 \mathbf{D}$$

Advanced Engineering Mathematics

Erwin Kreyszig 9th Edition

Chapter 7, Problem 3

Instant Answer

Solved by Expert Saurabh Kumar Gupta

12/25/2021

Step 1

For addition or subtraction of matrices, the matrices must have the same dimensions. Matrix A is a 3x3 matrix, Matrix C and D are 3x2 matrices, and Matrix B is a 3x3 matrix. Therefore, $\mathbf{A}+\mathbf{C}-\mathbf{D}$ and $\mathbf{B}+2 \mathbf{C}+4 \mathbf{D}$ Show more…

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Let $$\mathbf{A}=\left[\begin{array}{rrr}3 & 0 & 4 \\-1 & 2 & 2 \\6 & 5 & -4\end{array}\right], \mathbf{B}=\left[\begin{array}{rrr}0 & -5 & -3 \\-5 & 2 & 4 \\-3 & 4 & 0\end{array}\right],$$ $$\mathbf{C}=\left[\begin{array}{ll}0 & 2 \\2 & 4 \\1 & 3\end{array}\right], \quad \mathbf{D}=\left[\begin{array}{rr}6 & 1 \\-4 & 7 \\-8 & 3\end{array}\right],$$ $$\mathbf{u}=\left[\begin{array}{r}2 \\0 \\-1\end{array}\right], \quad\mathbf{v}=\left[\begin{array}{r}-45 \\0.8 \\1.2\end{array}\right].$$ Find the following expressions or give reasons why they are undefined. $$\mathbf{A}+\mathbf{C}-\mathbf{D}, \mathbf{C}-\mathbf{D}, \mathbf{D}-\mathbf{C}, \mathbf{B}+2 \mathbf{C}+4 \mathbf{D}$$

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Key Concepts

Matrix Addition and Subtraction

These operations are performed element-wise, meaning that for each corresponding position in the matrices, the numbers are added or subtracted. Consequently, both matrices must be conformable, i.e., have the same dimensions, otherwise the operation is undefined.

Scalar Multiplication

Scalar multiplication involves multiplying every element of a matrix by a constant. This operation is performed on individual matrices and does not affect the requirement that matrices be of the same size when subsequently adding or subtracting them.

Matrix Conformability

Matrix addition and subtraction are only defined when the matrices involved have identical dimensions. This means that each matrix must have the same number of rows and columns in order for the element-wise operations to be properly executed.

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