WBJEE · Maths · Determinants
If \(\left|\begin{array}{ccc}-1 & 7 & 0 \\ 2 & 1 & -3 \\ 3 & 4 & 1\end{array}\right|=A\). Then \(\left|\begin{array}{ccc}13 & -11 & 5 \\ -7 & -1 & 25 \\ -21 & -3 & -15\end{array}\right|\) is \begin{array}{l} \hline \end{array} \(\left(I_{3}\right.\) denotes the det of the identity matrix of order 3 )
- A \(A^{2}\)
- B \(A^{2}-A+1_{3}\)
- C \(A^{2}-3 A+l_{3}\)
- D \(3 A^{2}+5 A-4 l_{3}\)
Answer & Solution
Correct Answer
(A) \(A^{2}\)
Step-by-step Solution
Detailed explanation
We have. \[ \begin{aligned} A=&\left|\begin{array}{ccc} -1 & 7 & 0 \\ 2 & 1 & -3 \\ 3 & 4 & 1 \end{array}\right| \\ &=-1(1+12)-7(2+9) \\ &=-13-77=-90 \end{aligned} \] And let \(\quad B=\left|\begin{array}{ccc}13 & -11 & 5 \\ -7 & -1 & 25 \\ -21 & -3 & -15\end{array}\right|\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\mathrm{a}(\vec{\alpha} \times \vec{\beta})+\mathrm{b}(\vec{\beta} \times \vec{\gamma})+\mathrm{c}(\vec{\gamma} \times \vec{\alpha})=\overrightarrow{0}\), where \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are non-zero scalars, then the vectors \(\vec{\alpha}, \vec{\beta}, \vec{\gamma}\) areWBJEE 2021 Easy
- Let \(A\) and \(B\) are two independent events. The probability that both \(A\) and \(B\) happen is \(\frac{1}{12}\) and probability that neither A nor \(B\) happen is \(\frac{1}{2}\). ThenWBJEE 2023 Medium
- Reflection of the line \(\bar{a} z+a \bar{z}=0\) in the real axis is given byWBJEE 2023 Hard
- Let \(z_{1}, z_{2}\) be two fixed complex numbers in the argand plane and \(z\) be an arbitrary point satisfying \(\left|z-z_{1}\right|+\left|z-z_{2}\right|=2\left|z_{1}-z_{2}\right|\). Then, the locus of \(z\) will beWBJEE 2014 Hard
- Let \(\mathrm{f}:[0,1] \rightarrow \mathbb{R}\) and \(\mathrm{g}:[0,1] \rightarrow \mathbb{R}\) be defined as follows :
\(\left.\begin{array}{rl}
f(x) & =1 \text { if } x \text { is rational } \\
& =0 \text { if } x \text { is irrational }
\end{array}\right] \text { and }\)
\(\left.\begin{array}{rl}
g(x) & =0 \text { if } x \text { is rational } \\
& =1 \text { if } x \text { is irrational }
\end{array}\right] \text { then }\)WBJEE 2025 Medium - Let \(a, b, c\) be real numbers such that \(a+b+c < 0\) and the quadratic equation \(a x^{2}+b x+c=0\) has imaginary roots. Then.WBJEE 2019 Easy
More PYQs from WBJEE
- If angles \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are in A.P., then \(\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}\) is equal toWBJEE 2010 Hard
- Ferric ion forms a prussian blue precipitate due to the formation ofWBJEE 2018 Medium
- The units of surface tension and viscosity of liquids respectively areWBJEE 2015 Easy
- If the electron in a hydrogen atom jumps from an orbit with level \(\mathrm{n}_1=2\) to an orbit with level \(\mathrm{n}_2=1\) the emitted radiation has a wavelength given byWBJEE 2009 Easy
- If the algebraic sum of the distances from the points \((2,0),(0,2)\) and \((1,1)\) to a variable straight line be zero, then the line passes through the fixed pointWBJEE 2022 Medium
- A boy of mass \(40 \mathrm{~kg}\) is climbing a vertical pole at a constant speed. If the coefficient of friction between his palms and the pole is 0.8 and \(g=10 \mathrm{~m} / \mathrm{s}^2\), the horizontal force that he is applying on the pole isWBJEE 2010 Easy