Linear Algebra Quiz

What is given if you times a matrix by its inverse matrix?

• You get the identity matrix.

• B is the inverse of A.

• It is the equivalent if multiplying by 1.

• Redundancy and Inconsistency

When should you use Gaussian Elimination?

• When the number of columns in A is equal to the number of rows in B when we multiply A by B.

• When matrices are the same size.

• Is one where a very small change in coefficients leads to a very different solution. Sets of equations like this are to be avoided.

• When there are three or more variables to be found. It is much more effective than solving simultaneous equations.

When is a matrix said to be skew-symmetric?

• If A=A'. A symmetric matrix must always be square.

• In a similar way to the cross product. You take the values that aren't in that row.

• If A=(a b) then detA = ad-bc (c d)

• If A=-A'. It will always be square and have zeros in the diagonal.

How is the transpose of Matrix A written and formed?

• In a similar way to the cross product. You take the values that aren't in that row.

• Is one where a very small change in coefficients leads to a very different solution. Sets of equations like this are to be avoided.

• Transpose - A' and it is formed by swapping the rows and columns of matrix A. The first row of matrix A becomes the first column of A' etc.

• det A or |A|

What does it mean if the determinant is 0?

• If A=A'. A symmetric matrix must always be square.

• If the determinant is 0 then a matrix is singular.

• For any square matrix (same number of rows and columns).

• It is the equivalent if multiplying by 1.

When is a matrix said to be symmetric?

• If A=A'. A symmetric matrix must always be square.

• If the determinant is 0 then a matrix is singular.

• If A=(a b) then detA = ad-bc (c d)

• The matrices must be conformable.

What happens when you multiply a matrix by the identity matrix?

• You get the identity matrix.

• If the determinant is 0 then a matrix is singular.

• If it is redundant there is no unique solution but an infinite number of solutions. We are sometimes able to fix it by doing other row operations.

• It is the equivalent if multiplying by 1.

When can you add and subtract matrices?

• The matrices must be conformable.

• If A=(a b) then detA = ad-bc (c d)

• For any square matrix (same number of rows and columns).

• When matrices are the same size.

What is a full revolution around the origin?

• (1 0) (0 1)

• (1 0) (0 -1)

• (0 1) (-1 0)

• (-1 0) (0 -1)

How is the determinant of a matrix A be written?

• det A or |A|

• 1/detA (d - b) (-c a)

• (0 1) (-1 0)

• (1 0) (0 -1)