Special Matrices Quiz

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Questions and Answers

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?

<p>An element-wise operation (B)</p> Signup and view all the answers

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

<p>Matrices (C)</p> Signup and view all the answers

How are matrices added or subtracted?

<p>In an element-wise fashion (C)</p> 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?

<p>Rectangular matrix (C)</p> Signup and view all the answers

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

<p>The element-wise product of A and B (D)</p> Signup and view all the answers

What is the characteristic of an identity matrix?

<p>Diagonal elements are one (A)</p> Signup and view all the answers

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

<p>𝜶 𝑨 𝒊𝒋 (D)</p> Signup and view all the answers

What is the characteristic of a diagonal matrix?

<p>Non-diagonal elements are zero (A)</p> Signup and view all the answers

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

<p>Lower triangular matrix (A)</p> Signup and view all the answers

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

<p>Square matrix (B)</p> Signup and view all the answers

What is the condition for two matrices to be equal?

<p>The corresponding elements are equal (D)</p> Signup and view all the answers

What is the trace of a matrix A?

<p>The sum of all diagonal elements of A (C)</p> Signup and view all the answers

What is a symmetric matrix?

<p>A matrix that is equal to its transpose (D)</p> Signup and view all the answers

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

<p>ad - bc (D)</p> 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?

<p>A submatrix of the original matrix (B)</p> Signup and view all the answers

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