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Linear Algebra · College

Linear Algebra: Matrices Basics

Matrix operations, matrix types, and basic matrix algebra from a college linear algebra course.

35 cards · basic cards · AI-written, checked twice. Edit anything.

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What is a matrix?
A rectangular array of numbers arranged in rows and columns.
In matrix notation, what does a_ij represent?
The element in the i-th row and j-th column of matrix A.
What does it mean when a matrix has dimensions m by n?
The matrix has m rows and n columns.
What is a square matrix?
A matrix with the same number of rows and columns, where m equals n.
What is a row vector?
A matrix with exactly one row, with dimensions 1 by n.
What is a column vector?
A matrix with exactly one column, with dimensions m by 1.
What is the zero matrix?
A matrix where every element equals zero.
What is the identity matrix I_n?
An n by n matrix with ones on the main diagonal and zeros everywhere else.
What is a diagonal matrix?
A square matrix with non-zero elements only on the main diagonal.
What is an upper triangular matrix?
A square matrix where all entries below the main diagonal are zero.
What is a lower triangular matrix?
A square matrix where all entries above the main diagonal are zero.
When are two matrices equal?
When they have the same dimensions and all corresponding elements are equal.
What does it mean to multiply a matrix A by a scalar c?
Multiply every element of A by c.
What condition must be met to add two matrices?
The matrices must have the same dimensions.
How do you add two matrices A and B?
Add corresponding elements: (A + B)_ij = a_ij + b_ij.

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