Question bank: Matrix: Operations

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Question 1:

Easy

Given the matrix A = [[1, 2], [3, 4]] and the matrix B = [[-1, 0], [2, 1]], perform the operations of addition, subtraction, and multiplication between these matrices. Then, comment on the necessary conditions for addition and subtraction operations to be performed between matrices, and for matrix multiplication to be possible, express the product AB and comment on the associative property of this operation applied to matrices A, B, and the identity I = [[1, 0], [0, 1]].

Matrix: Operations

Multidisciplinary Question

Question 2:

Medium

Matrix: Operations

Question 3:

Medium

Matrix: Operations

Question 4:

Medium

Consider the following problematic context: in a study of urban traffic, a city hall collected data on the flow of vehicles at different intersections throughout a work week. Each intersection is represented by a vector of length seven, where each component corresponds to the number of vehicles that passed through on that day. When analyzing the data, it is necessary to perform various matrix operations to extract relevant information that can guide mobility policies. Let A and B be two matrices, where A represents the flow of vehicles at a set of intersections during Monday and B represents the flow during Tuesday. Knowing that matrix A is defined as: A = \begin{pmatrix} 200 & 180 & 150 & 220 & 190 & 210 & 205 \end{pmatrix}, and matrix B as: B = \begin{pmatrix} 220 & 190 & 195 & 215 & 205 & 190 & 225 \end{pmatrix}. (1) Calculate the resulting matrix from the sum of the flow of vehicles at each intersection between Monday and Tuesday. (2) Determine the resulting matrix from multiplying a scalar k = 1.1 by matrix A, representing a 10% increase in the flow of vehicles at all intersections during Monday. (3) Evaluate and discuss if the resulting matrix from item 1 is affected by the operation performed in item 2, and explain your reasoning.

Matrix: Operations

Theorical Question

Contextualized Question

Question 5:

Easy

Given the matrix A = [[1, 2, 3], [4, 5, 6]] and the matrix B = [[-1, -2, -3], [-4, -5, -6]], perform the sum of matrices A and B, and then calculate the product of the resulting matrix by the 3rd order identity matrix. Explain the concept of an identity matrix and the properties that characterize it.

Matrix: Operations

Contextualized Question

Calculus Question

IARA TIP

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