658 prompts matching "Why is matrix multiplication not commutative"
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Worked example: find the equation of a circle with centre (2,-1) and radius 4
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Worked example: find the centre and radius of the circle x^2+y^2-4x+6y-3=0
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Worked example: simplify (3+2i) + (1-5i)
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Worked example: simplify (2+i)(3-4i)
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Worked example: simplify (4+3i)/(1-2i)
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Worked example: find the modulus and argument of 3+4i
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Worked example: solve x^2+4x+13=0 giving the roots as complex numbers
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Worked example: find AB where A = [[1,2],[3,4]] and B = [[2,0],[1,3]]
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Worked example: find the determinant of [[5,2],[3,4]]
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Worked example: find the inverse of [[2,1],[5,3]]
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Worked example: use matrices to solve the simultaneous equations 2x+y=8 and x-y=1
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Worked example: find A+B and A-B where A = [[1,-2],[3,0]] and B = [[4,1],[-2,5]]
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Worked example: find the magnitude of the vector (3,4)
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Worked example: find a+b where a=(2,-1) and b=(-3,5)
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Worked example: find the angle between the vectors (1,2) and (3,-1) using the dot product
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Worked example: find the unit vector in the direction of (6,8)
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Worked example: find 2a-3b where a=(4,1) and b=(-2,3)
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Worked example: expand (x+2)^5 fully using the binomial theorem
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Worked example: find the term in x^3 in the expansion of (2x-1)^6
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Worked example: find the coefficient of x^4 in the expansion of (1+3x)^7
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