Find each sum or difference, if possible. [246]+[−2−4−6]\left[ \begin{matrix} 2 & 4 & 6 \end{matrix} \right] + \left[ \begin{matrix} -2 \\ -4 \\ -6 \end{matrix} \right]

Identify the dimensions of the matrices involved. A matrix has 3 rows and 1 column, while a matrix has 1 row and 3 columns. Recall that matrix addition or subtraction is only defined when both matrices have the same dimensions (i.e., the same number of rows and columns). Since the given matrices have different dimensions ( vs. ), they cannot be added or subtracted directly. Therefore, conclude that the sum or difference of these two matrices is not possible due to incompatible dimensions. If you want to perform operations involving these matrices, consider other operations like matrix multiplication, but addition and subtraction require matching dimensions.

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 29

Chapter 6, Problem 29

Find each sum or difference, if possible.
$[\begin{matrix} 2 & 4 & 6 \end{matrix}] + [\begin{matrix} - 2 \\ - 4 \\ - 6 \end{matrix}]$

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Identify the dimensions of the matrices involved. A <3x1> matrix has 3 rows and 1 column, while a <1x3> matrix has 1 row and 3 columns.

Recall that matrix addition or subtraction is only defined when both matrices have the same dimensions (i.e., the same number of rows and columns).

Since the given matrices have different dimensions (<3x1> vs. <1x3>), they cannot be added or subtracted directly.

Therefore, conclude that the sum or difference of these two matrices is not possible due to incompatible dimensions.

If you want to perform operations involving these matrices, consider other operations like matrix multiplication, but addition and subtraction require matching dimensions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix Dimensions and Compatibility

Matrix addition and subtraction require the matrices to have the same dimensions, meaning the same number of rows and columns. If the matrices differ in size, their sum or difference is undefined. Understanding this is crucial to determine if the operation is possible.

Matrix Addition and Subtraction

When two matrices have the same dimensions, their sum or difference is found by adding or subtracting corresponding elements. This operation is performed element-wise, resulting in a new matrix of the same size.

Matrix Notation and Representation

Matrices are represented by rows and columns, often denoted as m x n, where m is the number of rows and n is the number of columns. Recognizing the notation helps in visualizing the structure and performing operations correctly.

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Solve each system, using the method indicated.

x - z = -3

y + z = 6

2x - 3z = -9 (Gauss-Jordan)

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Solve each system by elimination. In systems with fractions, first clear denominators.

(2x-1)/3 + (y+2)/4 = 4

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Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

(3/8)x - (1/2)y = 7/8

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x⁵ + 3x⁴ - 3x³ - 2x² + x)/(2x² + 5x + 2)

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$3 x^{2} + 5 y^{2} = 17$

$2 x^{2} - 3 y^{2} = 5$

Find each sum or difference, if possible. [246]+[−2−4−6]\(\left\)[ \(\begin{matrix}\) 2 & 4 & 6 \(\end{matrix}\) \(\right\)] + \(\left\)[ \(\begin{matrix}\) -2 \\ -4 \\ -6 \(\end{matrix}\) \(\right\)]

Verified video answer for a similar problem:

Key Concepts

Matrix Dimensions and Compatibility

Matrix Addition and Subtraction

Matrix Notation and Representation

Find each sum or difference, if possible.
$[\begin{matrix} 2 & 4 & 6 \end{matrix}] + [\begin{matrix} - 2 \\ - 4 \\ - 6 \end{matrix}]$