Basic Linear Algebra Knowledge Test

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1. 1

   What is the scalar multiplication of a matrix?

   A Multiplying every element by the scalar. B Adding the scalar to each row. C Dividing every element by the scalar.
2. 2

   What is the identity matrix?

   A A matrix with 1s on the diagonal and 0s elsewhere. B A matrix with equal elements. C A matrix with 0s everywhere.
3. 3

   How do we find the inverse of a 2x2 matrix?

   A Switch rows and columns. B Multiply the matrix by a random scalar. C Swap the positions of a and d, and change the signs of b and c.
4. 4

   What is a row echelon form?

   A A row with all equal entries. B A matrix format where each row has more leading zeros than the previous row. C A matrix with non-zero rows.
5. 5

   What is the determinant of a 3x3 matrix?

   A The sum of diagonal elements. B A scalar value that is calculated from the elements of a square matrix. C The result of multiplying all rows.
6. 6

   What is the trace of a matrix?

   A The sum of the diagonal elements. B The sum of all elements. C The difference between maximum and minimum elements.
7. 7

   When is a matrix singular?

   A When all its elements are zero. B When there are negative elements. C When its determinant is zero.
8. 8

   What is the rank of a matrix?

   A Highest row index with all non-zero elements. B Number of zero rows. C The dimension of the vector space spanned by its rows or columns.
9. 9

   How is the transpose of a matrix obtained?

   A By multiplying it by a unit matrix. B By exchanging rows and columns. C By doubling all elements.
10. 10

    What is an orthogonal matrix?

    A A matrix whose transpose is its inverse. B A matrix with all zero diagonals. C A matrix with equal rows and columns.