Understanding M22 Vector Space

The video tutorial explains the M22 vector space, focusing on three key properties: the zero vector, the multiplicative identity, and the additive inverse. It begins by defining the zero vector as a 2x2 matrix with all zero entries. Next, it describes the multiplicative identity as the 2x2 identity matrix, which maintains the original matrix when multiplied. Finally, the tutorial covers the additive inverse, which is the negative of a given matrix, resulting in a zero vector when added to the original matrix. The video concludes with a brief summary.

What is the zero vector in the M22 vector space?

• A diagonal matrix with non-zero entries

• A matrix with alternating zero and one entries

• A two by two matrix with all zero entries

• A matrix with all entries as ones

Which of the following describes the multiplicative identity in the M22 vector space?

• A matrix with a diagonal of twos

• A matrix with all entries as ones

• A matrix with all zero entries

• A two by two identity matrix

What is the main property of the multiplicative identity in the M22 vector space?

• It changes the matrix it multiplies with

• It results in a zero matrix when multiplied

• It doubles the matrix it multiplies with

• It leaves the matrix unchanged when multiplied

What is the result of multiplying any matrix in M22 by the identity matrix?

• A matrix with all twos

• A matrix with all ones

• The original matrix

• A zero matrix

What is the main diagonal of the identity matrix in the M22 vector space?

• All zeros

• All twos

• Alternating zeros and ones

• All ones

What is the additive inverse of a given two by two matrix in the M22 vector space?

• A matrix with all entries as zero

• A matrix with all entries negated

• The same matrix with all entries doubled

• A matrix with all positive entries

How do you find the additive inverse of a matrix in the M22 vector space?

• Multiply the matrix by two

• Add one to each entry

• Transpose the matrix

• Negate each entry of the matrix

What happens when you add a matrix to its additive inverse in the M22 vector space?

• You get a matrix with all twos

• You get the original matrix

• You get a zero vector

• You get a matrix with all ones

Which property does the additive inverse satisfy in the M22 vector space?

• Matrix plus its inverse equals a matrix with all twos

• Matrix plus its inverse equals a matrix with all ones

• Matrix plus its inverse equals a zero vector

• Matrix plus its inverse equals the identity matrix