LINEAR ALGEBRA ORAL EXAM
QUESTIONS WITH COMPLETE
ANSWERS
what is an upper triangular matrix? - Answer-whenever a matrix has zeroes below the
main diagonal
what is an LU factorization of a matrix? - Answer-writing a matrix as a product of a lower
triangular matrix and an upper triangular matrix
how do you find the determinant of a 2x2 matrix? - Answer-multiplying the top left with
the bottom right and subtracting bottom left times top right.
what is the minor of a matrix with position (2, 3) - Answer-it is the determinant of a 2x2
matrix that results from deleting the 2nd row and 3rd column.
how do you find the determinant of a 3x3 matrix? - Answer-expanding and finding the
summations of all the elements times cofactors along any row or column.
what is the determinant of a triangular matrix? - Answer-product of diagonal entries
B is a matrix resulting from switching two rows of matrix A.
what is the determinant of B? - Answer-negative one times the determinant of A.
B is a resulting matrix from multiplying a row from matrix A by a scalar value. What is
the determinant of B? - Answer-the determinant of B is the scalar value times the
determinant of A.
B is a resulting matrix from matrix A when a row was multiplied by 4 and added to
another row. - Answer-the determinant of B is equal to the det of A.
if matrix A contains a row which is a multiple of another row, what is the det of A? -
Answer-0
A is an nxn matrix, what is the det of 7A? - Answer-the determinant is 7^n times det of
A.
what is the det of the inverse of a matrix? - Answer-the det is 1/det(matrix)
what is the det of the product of two matrices? - Answer-the det is the product of the two
determinants.
what is the det of the transpose of a matrix? - Answer-the same as the original matrix.
QUESTIONS WITH COMPLETE
ANSWERS
what is an upper triangular matrix? - Answer-whenever a matrix has zeroes below the
main diagonal
what is an LU factorization of a matrix? - Answer-writing a matrix as a product of a lower
triangular matrix and an upper triangular matrix
how do you find the determinant of a 2x2 matrix? - Answer-multiplying the top left with
the bottom right and subtracting bottom left times top right.
what is the minor of a matrix with position (2, 3) - Answer-it is the determinant of a 2x2
matrix that results from deleting the 2nd row and 3rd column.
how do you find the determinant of a 3x3 matrix? - Answer-expanding and finding the
summations of all the elements times cofactors along any row or column.
what is the determinant of a triangular matrix? - Answer-product of diagonal entries
B is a matrix resulting from switching two rows of matrix A.
what is the determinant of B? - Answer-negative one times the determinant of A.
B is a resulting matrix from multiplying a row from matrix A by a scalar value. What is
the determinant of B? - Answer-the determinant of B is the scalar value times the
determinant of A.
B is a resulting matrix from matrix A when a row was multiplied by 4 and added to
another row. - Answer-the determinant of B is equal to the det of A.
if matrix A contains a row which is a multiple of another row, what is the det of A? -
Answer-0
A is an nxn matrix, what is the det of 7A? - Answer-the determinant is 7^n times det of
A.
what is the det of the inverse of a matrix? - Answer-the det is 1/det(matrix)
what is the det of the product of two matrices? - Answer-the det is the product of the two
determinants.
what is the det of the transpose of a matrix? - Answer-the same as the original matrix.
