Top 50 Most Repeated DETERMINANTS PYQs | JEE MAINS
A curated collection of the most important questions from DETERMINANTS, fully solved with step-by-step concepts to prepare for JEE MAINS.
A curated collection of the most important questions from DETERMINANTS, fully solved with step-by-step concepts to prepare for JEE MAINS.
Compute $\det(A - \lambda I) = (3 - \lambda)(4 - \lambda) - (2)(1) = \lambda^2 - 7\lambda + 10$. The sum of roots of quadratic $a\lambda^2 + b\lambda ...
Read Full Step-by-Step Solution →Step 1: To find the determinant of a 3x3 matrix, we can use the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where a, b, c, d, e, f, g, h, ...
Read Full Step-by-Step Solution →Step 1: Recall the definition of the characteristic polynomial of a matrix. Step 2: Identify the correct expression for the characteristic polynomial ...
Read Full Step-by-Step Solution →Determinant of product is product of determinants....
Read Full Step-by-Step Solution →Expand along first row:
For any invertible square matrix, $M^{-1} = \frac{1}{\det M}\,\operatorname{adj}(M)$. This follows from the definition of the adjugate and the identit...
Read Full Step-by-Step Solution →Compute \(\det(B-\lambda I)\). Expanding the determinant gives \(-\lambda^{3}+10\lambda^{2}-27\lambda+58\), which after multiplying by \(-1\) yields t...
Read Full Step-by-Step Solution →Element $a_{23} = -2$. Cofactor $C_{23} = (-1)^{2+3} \cdot \text{det}(M_{23})$, where $M_{23}$ is minor. Remove row 2, column 3: $M_{23} = \begin{bmat...
Read Full Step-by-Step Solution →The area of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is given by: $ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 -...
Read Full Step-by-Step Solution →The determinant calculation gives 8 after substitutions. Taking absolute value and dividing by 2 yields 4. Common errors include omitting absolute val...
Read Full Step-by-Step Solution →Using the determinant-based area formula, the correct value is half the absolute value of the determinant sum. Common errors include forgetting to div...
Read Full Step-by-Step Solution →Compute $\det(A - \lambda I) = (3 - \lambda)(4 - \lambda) - (2)(1) = \lambda^2 - 7\lambda + 10$. The sum of roots of quadratic $a\lambda^2 + b\lambda ...
Read Full Step-by-Step Solution →Step 1: To find the determinant of a 3x3 matrix, we can use the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where a, b, c, d, e, f, g, h, ...
Read Full Step-by-Step Solution →Step 1: Recall the definition of the characteristic polynomial of a matrix. Step 2: Identify the correct expression for the characteristic polynomial ...
Read Full Step-by-Step Solution →Determinant of product is product of determinants....
Read Full Step-by-Step Solution →Expand along first row:
For any invertible square matrix, $M^{-1} = \frac{1}{\det M}\,\operatorname{adj}(M)$. This follows from the definition of the adjugate and the identit...
Read Full Step-by-Step Solution →Compute \(\det(B-\lambda I)\). Expanding the determinant gives \(-\lambda^{3}+10\lambda^{2}-27\lambda+58\), which after multiplying by \(-1\) yields t...
Read Full Step-by-Step Solution →Element $a_{23} = -2$. Cofactor $C_{23} = (-1)^{2+3} \cdot \text{det}(M_{23})$, where $M_{23}$ is minor. Remove row 2, column 3: $M_{23} = \begin{bmat...
Read Full Step-by-Step Solution →The area of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is given by: $ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 -...
Read Full Step-by-Step Solution →The determinant calculation gives 8 after substitutions. Taking absolute value and dividing by 2 yields 4. Common errors include omitting absolute val...
Read Full Step-by-Step Solution →Using the determinant-based area formula, the correct value is half the absolute value of the determinant sum. Common errors include forgetting to div...
Read Full Step-by-Step Solution →Compute $\det(A - \lambda I) = (3 - \lambda)(4 - \lambda) - (2)(1) = \lambda^2 - 7\lambda + 10$. The sum of roots of quadratic $a\lambda^2 + b\lambda ...
Read Full Step-by-Step Solution →Step 1: To find the determinant of a 3x3 matrix, we can use the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where a, b, c, d, e, f, g, h, ...
Read Full Step-by-Step Solution →Step 1: Recall the definition of the characteristic polynomial of a matrix. Step 2: Identify the correct expression for the characteristic polynomial ...
Read Full Step-by-Step Solution →Determinant of product is product of determinants....
Read Full Step-by-Step Solution →Expand along first row:
For any invertible square matrix, $M^{-1} = \frac{1}{\det M}\,\operatorname{adj}(M)$. This follows from the definition of the adjugate and the identit...
Read Full Step-by-Step Solution →Compute \(\det(B-\lambda I)\). Expanding the determinant gives \(-\lambda^{3}+10\lambda^{2}-27\lambda+58\), which after multiplying by \(-1\) yields t...
Read Full Step-by-Step Solution →Element $a_{23} = -2$. Cofactor $C_{23} = (-1)^{2+3} \cdot \text{det}(M_{23})$, where $M_{23}$ is minor. Remove row 2, column 3: $M_{23} = \begin{bmat...
Read Full Step-by-Step Solution →The area of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is given by: $ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 -...
Read Full Step-by-Step Solution →The determinant calculation gives 8 after substitutions. Taking absolute value and dividing by 2 yields 4. Common errors include omitting absolute val...
Read Full Step-by-Step Solution →Using the determinant-based area formula, the correct value is half the absolute value of the determinant sum. Common errors include forgetting to div...
Read Full Step-by-Step Solution →Compute $\det(A - \lambda I) = (3 - \lambda)(4 - \lambda) - (2)(1) = \lambda^2 - 7\lambda + 10$. The sum of roots of quadratic $a\lambda^2 + b\lambda ...
Read Full Step-by-Step Solution →Step 1: To find the determinant of a 3x3 matrix, we can use the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where a, b, c, d, e, f, g, h, ...
Read Full Step-by-Step Solution →Step 1: Recall the definition of the characteristic polynomial of a matrix. Step 2: Identify the correct expression for the characteristic polynomial ...
Read Full Step-by-Step Solution →Determinant of product is product of determinants....
Read Full Step-by-Step Solution →Expand along first row:
For any invertible square matrix, $M^{-1} = \frac{1}{\det M}\,\operatorname{adj}(M)$. This follows from the definition of the adjugate and the identit...
Read Full Step-by-Step Solution →Compute \(\det(B-\lambda I)\). Expanding the determinant gives \(-\lambda^{3}+10\lambda^{2}-27\lambda+58\), which after multiplying by \(-1\) yields t...
Read Full Step-by-Step Solution →Element $a_{23} = -2$. Cofactor $C_{23} = (-1)^{2+3} \cdot \text{det}(M_{23})$, where $M_{23}$ is minor. Remove row 2, column 3: $M_{23} = \begin{bmat...
Read Full Step-by-Step Solution →The area of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is given by: $ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 -...
Read Full Step-by-Step Solution →The determinant calculation gives 8 after substitutions. Taking absolute value and dividing by 2 yields 4. Common errors include omitting absolute val...
Read Full Step-by-Step Solution →Using the determinant-based area formula, the correct value is half the absolute value of the determinant sum. Common errors include forgetting to div...
Read Full Step-by-Step Solution →Compute $\det(A - \lambda I) = (3 - \lambda)(4 - \lambda) - (2)(1) = \lambda^2 - 7\lambda + 10$. The sum of roots of quadratic $a\lambda^2 + b\lambda ...
Read Full Step-by-Step Solution →Step 1: To find the determinant of a 3x3 matrix, we can use the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where a, b, c, d, e, f, g, h, ...
Read Full Step-by-Step Solution →