Q10Written answer
If A + B + C = 0, then prove that
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NCERT Exemplar · Class 12 · Maths
Chapter 4: Determinants
Practice each question, then open the answer or worked solution.
Questions
20 questionsQ11Written answer
If the co-ordinates of the vertices of an equilateral triangle with sides of length ‘a’ are (x1, y1),
(x2, y2), (x3, y3), then
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Q12Written answer
Find the value of q satisfying
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Q13Written answer
If , then find values of x.
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Q14Written answer
If a1, a2, a3, …, ar are in G.P., then prove that the determinant
is independent of r.
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Hence, the determinant is independent of r.
Q15Written answer
Show that the points (a + 5, a – 4), (a – 2, a + 3) and (a, a) do not lie on a straight line for any value of a.
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Worked solution
Given points are (a + 5, a – 4), (a – 2, a + 3) and (a, a).
Now, we have to prove that these points do not lie on a straight line.
So, if we prove that these points form a triangle then it can’t line on a straight line.
Hence, the given points form a triangle and can’t lie on a straight line.
Q16Written answer
Show that the DABC is an isosceles triangle if the determinant
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Q17Written answer
Find A–1 if and show that A-1 = (A2 – 3I)/ 2.
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Long Answer (L.A.)
Q18Written answer
If A = , find A-1.
Using A–1, solve the system of linear equations
x – 2y = 10 , 2x – y – z = 8 , –2y + z = 7.
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Q19Written answer
Using matrix method, solve the system of equations
3x + 2y – 2z = 3, x + 2y + 3z = 6, 2x – y + z = 2.
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Given system of equations are:
3x + 2y – 2z = 3
x + 2y + 3z = 6 and
2x – y + z = 2
Or,
AX = B
