Matrices, logarithms, and advanced trigonometry concepts tested on the harder ACT math questions, distinct from the core formulas deck.
35 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the result of adding two matrices of the same dimensions?
- Add corresponding elements in the same positions.
- When can you multiply two matrices together?
- When the number of columns in the first equals the number of rows in the second.
- What is the determinant of a 2x2 matrix [[a, b], [c, d]]?
- ad - bc
- What is the identity matrix I for 2x2 matrices?
- [[1, 0], [0, 1]]
- If a matrix A has determinant 0, what can you conclude about its inverse?
- The matrix has no inverse (it is singular).
- What is the transpose of a matrix?
- Swap rows and columns.
- When you multiply a matrix by scalar k, what happens?
- Every element in the matrix is multiplied by k.
- Is matrix multiplication commutative?
- No, AB does not generally equal BA.
- If A is a 3x2 matrix and B is a 2x4 matrix, what are the dimensions of AB?
- 3x4
- What does it mean if matrix A times matrix B equals the identity matrix I?
- B is the inverse of A (and A is the inverse of B).
- For a 2x2 matrix [[a, b], [c, d]], what is the inverse formula?
- (1/(ad - bc)) * [[d, -b], [-c, a]]
- What is the definition of logarithm: if b^x = y, then x = ?
- x = log_b(y)
- What is the product rule for logarithms?
- log_b(x) + log_b(y) = log_b(xy)
- What is the quotient rule for logarithms?
- log_b(x) - log_b(y) = log_b(x/y)
- What is the power rule for logarithms?
- log_b(x^n) = n * log_b(x)