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Recent questions tagged p121

Using properties of determinants, prove the following : $\begin{bmatrix} 1+a^2-b^2 & 2ab & -2b \\ 2ab & 1-a^2+b^2 & 2a \\ 2b & -2a & 1-a^2=b^2 \end{bmatrix} = (1 + a^2 + b^2)^3. $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove that : $ \begin{bmatrix} a^2+1 & ab & ac \\ ab & b^2+1 & bc \\ ca & cb & c^2+1 \end{bmatrix} = (1+a^2+b^2+c^2) $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Which of the following is correct:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Let $A$ be a square matrix of order $3 \times 3$, then $ |kA|$ is equal to:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} a^2+1&ab&ac \\ ab&b^2+1&bc \\ ca&cb&c^2+1 \end{vmatrix} = 1+a^2+b^2+c^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1+a^2-b^2&2ab&-2b \\ 2ab&1-a^2+b^2&2a \\ 2b&-2a&1-a^2-b^2 \end{vmatrix} = (1+a^2+b^2)^3 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1&x&x^2 \\ x^2&1&x \\ x&x^2&1 \end{vmatrix} = (1-x^3)^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

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