PRE CALCULUS Matrices and Vectors

Question 1

What is the determinant of the matrix [[3, 1], [2, 4]]?

Accepted Answer

10

Answer

The determinant of a 2×2 matrix [[a,b],[c,d]] is ad − bc = (3)(4) − (1)(2) = 10.

Question 2

Which operation is NOT defined for matrices A and B?

Accepted Answer

A + B when dimensions differ

Answer

Matrix addition requires both matrices to have identical dimensions.

Question 3

What is the result of multiplying a 2×3 matrix by a 3×4 matrix?

Accepted Answer

2×4 matrix

Answer

When multiplying an m×n matrix by an n×p matrix, the result is an m×p matrix, so 2×4.

Question 4

What is the identity matrix for 2×2 multiplication?

Accepted Answer

[[1,0],[0,1]]

Answer

The identity matrix has 1s on the main diagonal and 0s elsewhere, leaving any matrix unchanged when multiplied.

Question 5

If vector u = ⟨3, −4⟩, what is |u|?

Accepted Answer

5

Answer

The magnitude of vector ⟨a, b⟩ is √(a² + b²) = √(9 + 16) = √25 = 5.

PRE CALCULUS Practice Test