BMath Bachelor of Mathematics Linear Algebra and Matrix Theory 3

Question 1

What is the inner product (dot product) of vectors u = (1, 2, 3) and v = (4, 5, 6)?

Accepted Answer

32

Answer

14

Answer

18

Answer

12

Question 2

The Gram-Schmidt process is used to:

Accepted Answer

Convert a basis into an orthonormal basis

Answer

Diagonalize a matrix

Answer

Find eigenvalues

Answer

Compute the determinant

Question 3

For an n×n matrix, the characteristic polynomial is of degree:

Accepted Answer

n

Answer

n − 1

Answer

n + 1

Answer

2n

Question 4

Cramer's Rule provides a formula for solving Ax = b using:

Accepted Answer

Ratios of determinants

Answer

Matrix multiplication

Answer

Eigenvalue decomposition

Answer

The trace of A

Question 5

A matrix A is diagonalizable if and only if:

Accepted Answer

It has n linearly independent eigenvectors

Answer

It is symmetric

Answer

Its determinant is 1

Answer

All its entries are distinct

Question 6

The dimension of the null space of an m×n matrix A plus the rank of A equals:

Accepted Answer

n

Answer

m

Answer

m + n

Answer

m × n