Chapter 5 Flashcards
- Which of the following is true about a symmetric matrix?
A) It has the same elements across its diagonal.
B) It is equal to its transpose.
C) It is a square matrix.
D) Both B and C.
D) Both B and C.
- What is the identity matrix?
A) A square matrix with all elements equal to 1.
B) A square matrix with 1s on the diagonal and 0s elsewhere.
C) A matrix where every row is identical.
D) A matrix with its determinant equal to zero.
B) A square matrix with 1s on the diagonal and 0s elsewhere.
What is a matrix inverse A^-1?
A) A matrix that, when multiplied by A, results in the identity matrix.
B) A matrix that has no determinant.
C) A matrix whose transpose equals itself.
D) A square matrix with no zero elements.
A) A matrix that, when multiplied by A, results in the identity matrix.
- What is the result of multiplying a matrix A by a scalar k?
A) A matrix with each element multiplied by k.
B) A matrix with k added to each element.
C) A matrix with k as its determinant.
D) None of the above.
A) A matrix with each element multiplied by k.
When is matrix multiplication defined?
A) The number of rows in the first matrix equals the number of columns in the second matrix.
B) The number of columns in the first matrix equals the number of rows in the second matrix.
C) Both matrices must be square matrices.
D) Both matrices must have the same dimensions.
B) The number of columns in the first matrix equals the number of rows in the second matrix.
Which of the following is true for matrix addition?
A) The matrices must have the same number of rows and columns.
B) The matrices must be square matrices.
C) The matrices must have the same determinant.
D) The matrices must be invertible.
A) The matrices must have the same number of rows and columns.
Which of the following is not an allowable elementary row operation?
A) Switching any two rows.
B) Multiplying a row by zero.
C) Adding a multiple of one row to another row.
D) Multiplying all elements in a row by a non-zero scalar.
B) Multiplying a row by zero.
What is the main goal of Gaussian elimination?
A) To find the transpose of a matrix.
B) To compute the determinant of a matrix.
C) To reduce the matrix to row echelon form or solve a system of linear equations.
D) To find the matrix inverse.
C) To reduce the matrix to row echelon form or solve a system of linear equations.
ow can the inverse of a matrix be determined using Gaussian elimination?
A) By augmenting the matrix with the identity matrix and performing row operations.
B) By computing the determinant and dividing by each element.
C) By taking the transpose of the matrix.
D) None of the above.
A) By augmenting the matrix with the identity matrix and performing row operations.
Which of the following is true about Boolean addition in matrices?
A) Boolean addition is the same as standard matrix addition.
B) Boolean addition is equivalent to taking the logical AND of corresponding elements.
C) Boolean addition is equivalent to taking the logical OR of corresponding elements.
D) Boolean addition is not defined for matrices.
C) Boolean addition is equivalent to taking the logical OR of corresponding elements.
In Boolean matrix multiplication, how are elements of the resulting matrix computed?
A) By summing the products of corresponding elements.
B) By taking the logical AND of row elements and column elements, followed by a logical OR.
C) By taking the logical OR of row elements and column elements, followed by a logical AND.
D) By using scalar multiplication of Boolean values.
B) By taking the logical AND of row elements and column elements, followed by a logical OR.
What is a Boolean matrix?
A) A matrix where every element is either 0 or 1.
B) A matrix with elements that can only be negative.
C) A matrix used only for finding determinants.
D) A matrix that is always symmetric.
A) A matrix where every element is either 0 or 1.
