Top 50 Most Repeated MATRICES PYQs | JEE MAINS
A curated collection of the most important questions from MATRICES, fully solved with step-by-step concepts to prepare for JEE MAINS.
A curated collection of the most important questions from MATRICES, fully solved with step-by-step concepts to prepare for JEE MAINS.
After row reduction, $A^{-1} = \begin{bmatrix}-2 & 1\\1.5 & -0.5\end{bmatrix}$; (1,1) entry is -2....
Read Full Step-by-Step Solution →A skew‑symmetric matrix has zeros on the diagonal and opposite off‑diagonal entries. Option 3 satisfies $a_{ij} = -a_{ji}$ and has zero diagonal entri...
Read Full Step-by-Step Solution →Determinant $\det A = 2\times4 - 3\times1 = 5$. The adjugate matrix is $\begin{pmatrix} 4 & -3 \\ -1 & 2 \end{pmatrix}$. Hence $A^{-1}=\frac{1}{5}\tex...
Read Full Step-by-Step Solution →Determinant is 1. Swap diagonal elements, change sign of off-diagonal....
Read Full Step-by-Step Solution →Adding a multiple of a row to another leaves determinant unchanged....
Read Full Step-by-Step Solution →Elementary row operations are used to transform a matrix into row echelon form. Elementary column operations are used to transform a matrix into colum...
Read Full Step-by-Step Solution →A matrix $A$ is symmetric if $A = A^T$ and skew-symmetric if $A = -A^T$. For both, $A = -A \Rightarrow 2A = 0 \Rightarrow A = 0$. Only the zero matrix...
Read Full Step-by-Step Solution →$(A^T)^T = A$. Transpose twice returns original matrix....
Read Full Step-by-Step Solution →Let $B = A - A'$. Then $B' = A' - A = -(A - A') = -B$....
Read Full Step-by-Step Solution →The symmetric and skew-symmetric decomposition of a matrix $A$ is given by $A = \frac{1}{2}(A + A^T) + \frac{1}{2}(A - A^T)$....
Read Full Step-by-Step Solution →For any square matrix, the trace equals the sum of eigenvalues, the determinant equals the product of eigenvalues, and the rank equals the count of no...
Read Full Step-by-Step Solution →The Cayley-Hamilton theorem states that a matrix satisfies its own characteristic equation. For matrix $A$, the characteristic polynomial is $\det(A -...
Read Full Step-by-Step Solution →Matrix addition is element-wise; adding identity matrix increases diagonal elements by 1....
Read Full Step-by-Step Solution →By Cayley-Hamilton theorem, every matrix satisfies its characteristic equation $ A^2 - 5A + 6I = 0 $....
Read Full Step-by-Step Solution →When a matrix is scaled by k, its determinant scales by kⁿ where n is matrix size. For 3×3 matrix scaled by 2: 2³ × 5 = 8 × 5 = 40...
Read Full Step-by-Step Solution →This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Matrices....
Read Full Step-by-Step Solution →Determinants follow the multiplicative property: det(AB) = det(A) × det(B). Adding determinants (3+4=7) is incorrect. Concatenating digits (34) and ov...
Read Full Step-by-Step Solution →The determinant of a product of matrices equals the product of their determinants. Common errors include adding determinants (3 + (-2) = 1) or ignorin...
Read Full Step-by-Step Solution →After row reduction, $A^{-1} = \begin{bmatrix}-2 & 1\\1.5 & -0.5\end{bmatrix}$; (1,1) entry is -2....
Read Full Step-by-Step Solution →A skew‑symmetric matrix has zeros on the diagonal and opposite off‑diagonal entries. Option 3 satisfies $a_{ij} = -a_{ji}$ and has zero diagonal entri...
Read Full Step-by-Step Solution →Determinant $\det A = 2\times4 - 3\times1 = 5$. The adjugate matrix is $\begin{pmatrix} 4 & -3 \\ -1 & 2 \end{pmatrix}$. Hence $A^{-1}=\frac{1}{5}\tex...
Read Full Step-by-Step Solution →Determinant is 1. Swap diagonal elements, change sign of off-diagonal....
Read Full Step-by-Step Solution →Adding a multiple of a row to another leaves determinant unchanged....
Read Full Step-by-Step Solution →Elementary row operations are used to transform a matrix into row echelon form. Elementary column operations are used to transform a matrix into colum...
Read Full Step-by-Step Solution →A matrix $A$ is symmetric if $A = A^T$ and skew-symmetric if $A = -A^T$. For both, $A = -A \Rightarrow 2A = 0 \Rightarrow A = 0$. Only the zero matrix...
Read Full Step-by-Step Solution →$(A^T)^T = A$. Transpose twice returns original matrix....
Read Full Step-by-Step Solution →Let $B = A - A'$. Then $B' = A' - A = -(A - A') = -B$....
Read Full Step-by-Step Solution →The symmetric and skew-symmetric decomposition of a matrix $A$ is given by $A = \frac{1}{2}(A + A^T) + \frac{1}{2}(A - A^T)$....
Read Full Step-by-Step Solution →For any square matrix, the trace equals the sum of eigenvalues, the determinant equals the product of eigenvalues, and the rank equals the count of no...
Read Full Step-by-Step Solution →The Cayley-Hamilton theorem states that a matrix satisfies its own characteristic equation. For matrix $A$, the characteristic polynomial is $\det(A -...
Read Full Step-by-Step Solution →Matrix addition is element-wise; adding identity matrix increases diagonal elements by 1....
Read Full Step-by-Step Solution →By Cayley-Hamilton theorem, every matrix satisfies its characteristic equation $ A^2 - 5A + 6I = 0 $....
Read Full Step-by-Step Solution →When a matrix is scaled by k, its determinant scales by kⁿ where n is matrix size. For 3×3 matrix scaled by 2: 2³ × 5 = 8 × 5 = 40...
Read Full Step-by-Step Solution →This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Matrices....
Read Full Step-by-Step Solution →Determinants follow the multiplicative property: det(AB) = det(A) × det(B). Adding determinants (3+4=7) is incorrect. Concatenating digits (34) and ov...
Read Full Step-by-Step Solution →The determinant of a product of matrices equals the product of their determinants. Common errors include adding determinants (3 + (-2) = 1) or ignorin...
Read Full Step-by-Step Solution →After row reduction, $A^{-1} = \begin{bmatrix}-2 & 1\\1.5 & -0.5\end{bmatrix}$; (1,1) entry is -2....
Read Full Step-by-Step Solution →A skew‑symmetric matrix has zeros on the diagonal and opposite off‑diagonal entries. Option 3 satisfies $a_{ij} = -a_{ji}$ and has zero diagonal entri...
Read Full Step-by-Step Solution →Determinant $\det A = 2\times4 - 3\times1 = 5$. The adjugate matrix is $\begin{pmatrix} 4 & -3 \\ -1 & 2 \end{pmatrix}$. Hence $A^{-1}=\frac{1}{5}\tex...
Read Full Step-by-Step Solution →Determinant is 1. Swap diagonal elements, change sign of off-diagonal....
Read Full Step-by-Step Solution →Adding a multiple of a row to another leaves determinant unchanged....
Read Full Step-by-Step Solution →Elementary row operations are used to transform a matrix into row echelon form. Elementary column operations are used to transform a matrix into colum...
Read Full Step-by-Step Solution →A matrix $A$ is symmetric if $A = A^T$ and skew-symmetric if $A = -A^T$. For both, $A = -A \Rightarrow 2A = 0 \Rightarrow A = 0$. Only the zero matrix...
Read Full Step-by-Step Solution →$(A^T)^T = A$. Transpose twice returns original matrix....
Read Full Step-by-Step Solution →Let $B = A - A'$. Then $B' = A' - A = -(A - A') = -B$....
Read Full Step-by-Step Solution →The symmetric and skew-symmetric decomposition of a matrix $A$ is given by $A = \frac{1}{2}(A + A^T) + \frac{1}{2}(A - A^T)$....
Read Full Step-by-Step Solution →For any square matrix, the trace equals the sum of eigenvalues, the determinant equals the product of eigenvalues, and the rank equals the count of no...
Read Full Step-by-Step Solution →The Cayley-Hamilton theorem states that a matrix satisfies its own characteristic equation. For matrix $A$, the characteristic polynomial is $\det(A -...
Read Full Step-by-Step Solution →Matrix addition is element-wise; adding identity matrix increases diagonal elements by 1....
Read Full Step-by-Step Solution →By Cayley-Hamilton theorem, every matrix satisfies its characteristic equation $ A^2 - 5A + 6I = 0 $....
Read Full Step-by-Step Solution →