SATHEE: Matrices and Determinants 2 Question 25

Matrices and Determinants 2 Question 25

28. The value of the determinant $| \begin{matrix} 1 & a & a^{2} - b c \\ 1 & b & b^{2} - c a \\ 1 & c & c^{2} - a b \end{matrix} |$ is ….

$(1988, 2 M)$

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Answer:

Correct Answer: 27. (0)

Solution:

$| \begin{matrix} 1 & a & a^{2} - b c \\ 1 & b & b^{2} - c a \\ 1 & c & c^{2} - a b \end{matrix} | = | \begin{matrix} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{matrix} | - | \begin{matrix} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{matrix} |$

Now, $| \begin{matrix} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{matrix} | = \frac{1}{a b c} | \begin{matrix} a & a^{2} & a b c \\ b & b^{2} & a b c \\ c & c^{2} & a b c \end{matrix} |$

Applying $R_{1} \to a R_{1}, R_{2} \to b R_{2}, R_{3} \to c R_{3}$

$\begin{aligned} = \frac{1}{a b c} \cdot a b c | \begin{array}{c} a & a^{2} & 1 \\ b & b^{2} & 1 \\ c & c^{2} & 1 \end{array} | = | \begin{array}{c} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{array} | \\ ∴ | \begin{array}{c} 1 & a & a^{2} - b c \\ 1 & b & b^{2} - c a \\ 1 & c & c^{2} - a b \end{array} | & = 0 \end{aligned}$

Matrices and Determinants 2 Question 25

28. The value of the determinant $| \begin{matrix} 1 & a & a^{2} - b c \\ 1 & b & b^{2} - c a \\ 1 & c & c^{2} - a b \end{matrix} |$ is ….

Answer:

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Matrices and Determinants 2 Question 25

28. The value of the determinant |1aa2−bc1bb2−ca1cc2−ab| is ….

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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28. The value of the determinant $| \begin{matrix} 1 & a & a^{2} - b c \\ 1 & b & b^{2} - c a \\ 1 & c & c^{2} - a b \end{matrix} |$ is ….