Find each sum or difference, if possible. [−43]−[582]\left[ \begin{matrix} -4 & 3 \end{matrix} \right] - \left[ \begin{matrix} 5 & 8 & 2 \end{matrix} \right]

Ch. 5 - Systems and Matrices

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 35

Chapter 6, Problem 35

Find each sum or difference, if possible.
$[\begin{matrix} - 4 & 3 \end{matrix}] - [\begin{matrix} 5 & 8 & 2 \end{matrix}]$

Verified step by step guidance

Identify the dimensions of each matrix. The first matrix is a 1x2 matrix (1 row, 2 columns), and the second matrix is a 1x3 matrix (1 row, 3 columns).

Recall that matrix addition or subtraction is only possible when the two matrices have the same dimensions, meaning the same number of rows and columns.

Since the first matrix has 2 columns and the second matrix has 3 columns, their dimensions do not match.

Conclude that the subtraction of a 1x3 matrix from a 1x2 matrix is not defined because their sizes are different.

Therefore, the sum or difference cannot be performed in this case.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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, such as a 1x2 matrix and a 1x3 matrix, their sum or difference is undefined because corresponding elements do not align.

Matrix Addition and Subtraction

To add or subtract matrices, you perform the operation element-wise, combining corresponding entries from each matrix. This process is only valid when both matrices share identical dimensions, ensuring each element has a matching counterpart.

Understanding Matrix Notation

A matrix is described by its dimensions, rows by columns (e.g., 1x2 means 1 row and 2 columns). Recognizing this notation helps determine if operations like addition or subtraction are possible and guides how to perform them correctly.

Recommended video:

05:18

Interval Notation

Related Practice

Textbook Question

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary.

5x - 5y - 3 = 0

x - y - 12 = 0

Textbook Question

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

$5 x^{2} - 2 y^{2} = 25$

$10 x^{2} + y^{2} = 50$

views

Textbook Question

Find each sum or difference, if possible. See Examples 2 and 3.

views

Textbook Question

Evaluate each determinant.

$∣ \begin{matrix} - 1 & 8 \\ 2 & 9 \end{matrix} ∣$

Textbook Question

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-x⁴ - 8x² + 3x - 10)/((x + 2)(x² + 4)²)

Find each sum or difference, if possible. [−43]−[582]\(\left\)[ \(\begin{matrix}\) -4 & 3 \(\end{matrix}\) \(\right\)] - \(\left\)[ \(\begin{matrix}\) 5 & 8 & 2 \(\end{matrix}\) \(\right\)]

Verified video answer for a similar problem:

Key Concepts

Matrix Dimensions and Compatibility

Matrix Addition and Subtraction

Understanding Matrix Notation

Find each sum or difference, if possible.
$[\begin{matrix} - 4 & 3 \end{matrix}] - [\begin{matrix} 5 & 8 & 2 \end{matrix}]$