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Mathematics · Class 10
Add component-wise: (x1 i + y1 j) + (x2 i + y2 j) = (x1+x2)i + (y1+y2)j. Subtract likewise. k u stretches (or shrinks) by |k| and reverses if k<0. The parallelogram (or triangle) law is the picture of the same addition.
PracticeAdd or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are entry-wise, not row-dot-column (that is multiplication).
PracticeThe angle between a tangent and a chord equals the angle in the alternate (other) segment of the circle. If the tangent-chord angle is 46 deg, the inscribed angle in the alternate segment is 46 deg. This is not 'half the angle' and not automatically 90.
PracticeFor an acute given angle A, let a be its opposite side, b the other known side, and h = b sin A. If a < h, no triangle exists. If a = h, there is one right triangle. If h < a < b, there are two triangles. If a >= b, there is one triangle.