WBJEE · Maths · Matrices
Let \(A\) be a square matrix of order 3 whose all entries are 1 and let \(I_{3}\) be the identity matrix of order \(3 .\) Then, the matrix \(A-3 I_{3}\) is
- A invertible
- B orthogonal
- C non-invertible
- D real Skew Symmetric matrix
Answer & Solution
Correct Answer
(C) non-invertible
Step-by-step Solution
Detailed explanation
Given, that \(A-3 J_{3}\) \[ =\left[\begin{array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right]-3\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] \]…
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
- The locus of points \((x, y)\) in the plane satisfying \(\sin ^2 x+\sin ^2 y=1\) consists ofWBJEE 2023 Hard
- The unit vector in ZOX plane, making angles \(45^{\circ}\) and \(60^{\circ}\) respectively with \(\vec{\alpha}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{\beta}=j-\hat{k}\) isWBJEE 2020 Medium
- The vertex of the parabola \(y^2+6 x-2 y+13=0\) is
\(\begin{aligned}
& (y-1)^2=-6 x-12 \\
& (y-1)^2=-6(x+2)=4\left(\frac{-6}{4}\right)(x+2) \\
& \text { Vertex } \rightarrow(-2,1)
\end{aligned}\)WBJEE 2011 Easy - Number of intersecting points of the conics \(4 x^{2}+9 y^{2}=1\) and \(4 x^{2}+y^{2}=4\) isWBJEE 2015 Easy
- If the equation \(x^{2}-ca+d=0\) has roots equal to the fourth powers of the roots of \(x^{2}+a x+b=0,\) where \(a^{2}>4 b,\) then the roots of \(x^{2}-4 b x+2 b^{2}-c=0\) will beWBJEE 2018 Medium
- The equation of the plane through the point \((2,-1,-3)\) and parallel to the lines \(\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}\) and \(\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}\) isWBJEE 2020 Medium
More PYQs from WBJEE
- If \(\mathrm{a}=2 \sqrt{2}, \mathrm{~b}=6, \mathrm{~A}=45^{\circ}\), thenWBJEE 2009 Medium
- If \(\sqrt{y}=\cos ^{-1} x\), then it satisfies the differential equation \(\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}=c,\) where \(c\) is equal toWBJEE 2014 Medium
- Monochromatic light of wavelength \(\lambda=4770 Ã…\) is incident separately on the surface of four different metals \(A, B, C\) and D. The work functions of \(A, B, C\) and D are \(4.2 \mathrm{eV}, 3.7 \mathrm{eV}, 3.2 \mathrm{eV}\) and 2.3 eV , respectively. The metal / metals from which electrons will be emitted is /areWBJEE 2024 Easy
- The length of the chord of the parabola \(y^{2}=4 a x(a>0)\) which passes through the vertex and makes an acute angle \(\alpha\) with the axis of the parabola isWBJEE 2020 Medium
- A positive acute angle is divided into two parts whose tangents are \(\frac{1}{2}\) and \(\frac{1}{3}\). Then the angle isWBJEE 2009 Easy
- The figure represents two equipotential lines in \(\mathrm{x}-\mathrm{y}\) plane for an electric field. The \(\mathrm{x}\)-component \(\mathrm{E}_{\mathrm{x}}\) of the electric field in space between these equipotential lines is,
WBJEE 2023 Easy