Special Matrices Quiz

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What is the condition for a square matrix to be symmetric?

It is equal to its transpose (correct)

It has only one row

Its determinant is zero

It has only one column

What type of matrix has all elements equal to zero?

Diagonal matrix

Design matrix

Null or zero matrix (correct)

Scalar matrix

What is a design matrix used for?

To find the determinant of a matrix

To perform matrix operations

To store data about multiple characteristics (correct)

To find the inverse of a matrix

What is the result of matrix-scalar multiplication?

An element-wise operation Signup and view all the answers

What is the primary way computers interact with data in practice?

Matrices Signup and view all the answers

How are matrices added or subtracted?

In an element-wise fashion Signup and view all the answers

What is the term for a matrix with the number of rows not equal to the number of columns?

Rectangular matrix Signup and view all the answers

What is the Hadamard product of two matrices A and B?

The element-wise product of A and B Signup and view all the answers

What is the characteristic of an identity matrix?

Diagonal elements are one Signup and view all the answers

What is the result of multiplying each element of a matrix A by a scalar 𝜶?

𝜶 𝑨 𝒊𝒋 Signup and view all the answers

What is the characteristic of a diagonal matrix?

Non-diagonal elements are zero Signup and view all the answers

What type of matrix has elements above the main diagonal equal to zero?

Lower triangular matrix Signup and view all the answers

What is the term for a matrix with the number of rows equal to the number of columns?

Square matrix Signup and view all the answers

What is the condition for two matrices to be equal?

The corresponding elements are equal Signup and view all the answers

What is the trace of a matrix A?

The sum of all diagonal elements of A Signup and view all the answers

What is a symmetric matrix?

A matrix that is equal to its transpose Signup and view all the answers

What is the determinant of a 2×2 matrix [[a, b], [c, d]]?

ad - bc Signup and view all the answers

What is the minor of a matrix obtained by removing the row and column associated with the indices i and j?

A submatrix of the original matrix Signup and view all the answers