Decide whether the matrix [[3, 2], [5, 3]] is invertible.
Correct answer(s):
- invertible
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Find the determinant of the matrix [[6, 6], [6, 6]].
Correct answer(s):
- 0
Decide whether the matrix [[-3, -4], [4, -3]] is invertible.
Correct answer(s):
- invertible
Decide whether the matrix [[6, -2], [6, -4]] is invertible.
Correct answer(s):
- invertible
Find the determinant of the matrix [[0, -3], [-3, 5]].
Correct answer(s):
- -9
Decide whether the matrix [[6, 5], [0, 6]] is invertible.
Correct answer(s):
- invertible
Decide whether the matrix [[0, 0], [-5, 4]] is invertible.
Correct answer(s):
- not invertible
Find the determinant of the matrix [[-1, 3], [6, 6]].
Correct answer(s):
- -24
In the expansion of (1x + 1y)^7, find the coefficient of x^1y^6.
Correct answer(s):
- 7
In the expansion of (2x + 1y)^12, find the coefficient of x^11y^1.
Correct answer(s):
- 24576
In the expansion of (3x + 1y)^9, find the coefficient of x^3y^6.
Correct answer(s):
- 2268
In the expansion of (1x + 1y)^8, find the coefficient of x^7y^1.
Correct answer(s):
- 8
In the expansion of (1x + 1y)^9, find the coefficient of x^7y^2.
Correct answer(s):
- 36
In the expansion of (1x + 2y)^8, find the coefficient of x^6y^2.
Correct answer(s):
- 112
In the expansion of (2x + -1y)^11, find the coefficient of x^7y^4.
Correct answer(s):
- 42240
In the expansion of (2x + 1y)^10, find the coefficient of x^5y^5.
Correct answer(s):
- 8064
In the expansion of (1x + 1y)^11, find the coefficient of x^2y^9.
Correct answer(s):
- 55
In the expansion of (3x + 1y)^6, find the coefficient of x^3y^3.
Correct answer(s):
- 540
In the expansion of (3x + 1y)^6, find the coefficient of x^1y^5.
Correct answer(s):
- 18
In the expansion of (1x + -1y)^10, find the coefficient of x^3y^7.
Correct answer(s):
- -120