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?
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Add corresponding elements in the same positions.- When can you multiply two matrices together?
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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]]?
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ad - bc- What is the identity matrix I for 2x2 matrices?
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[[1, 0], [0, 1]]- If a matrix A has determinant 0, what can you conclude about its inverse?
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The matrix has no inverse (it is singular).- What is the transpose of a matrix?
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Swap rows and columns.- When you multiply a matrix by scalar k, what happens?
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Every element in the matrix is multiplied by k.- Is matrix multiplication commutative?
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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?
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3x4- What does it mean if matrix A times matrix B equals the identity matrix I?
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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?
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(1/(ad - bc)) * [[d, -b], [-c, a]]- What is the definition of logarithm: if b^x = y, then x = ?
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x = log_b(y)- What is the product rule for logarithms?
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log_b(x) + log_b(y) = log_b(xy)- What is the quotient rule for logarithms?
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log_b(x) - log_b(y) = log_b(x/y)- What is the power rule for logarithms?
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log_b(x^n) = n * log_b(x)
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