If b and c are non-zero real numbers,A = begi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given matrices $A = \begin{bmatrix} 1 & b & c \ b & 2 & 3 \ c & 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & b & c \ -b & 0 & 2 \ -c & -2

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Given matrices $A = \begin{bmatrix} 1 & b & c \ b & 2 & 3 \ c & 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & b & c \ -b & 0 & 2 \ -c & -2 & 0 \end{bmatrix}$.First,we calculate the sum $A+B$:$A+B = \begin{bmatrix} 1+0 & b+b & c+c \ b-b & 2+0 & 3+2 \ c-c & 3-2 & 4+0 \end{bmatrix} = \begin{bmatrix} 1 & 2b & 2c \ 0 & 2 & 5 \ 0 & 1 & 4 \end{bmatrix}$.Now,we find the determinant of the resulting matrix:$\det(A+B) = \begin{vmatrix} 1 & 2b & 2c \ 0 & 2 & 5 \ 0 & 1 & 4 \end{vmatrix}$.Expanding along the first column:$\det(A+B) = 1 	imes \begin{vmatrix} 2 & 5 \ 1 & 4 \end{vmatrix} - 0 + 0 = 1 	imes (2 	imes 4 - 5 	imes 1) = 1 	imes (8 - 5) = 3$.

If $b$ and $c$ are non-zero real numbers,$A = \begin{bmatrix} 1 & b & c \\ b & 2 & 3 \\ c & 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0 \end{bmatrix}$,then $\det(A+B) = $

Similar Questions

If $a, b$ and $c$ are real numbers,and $\Delta=\begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c \\ a+b & b+c & c+a \end{vmatrix}=0$,show that either $a+b+c=0$ or $a=b=c$.

If $A, B, C$ are the angles of a triangle and $\left| {\begin{array}{*{20}{c}}1&1&1\\{1 + \sin A}&{1 + \sin B}&{1 + \sin C}\\{\sin A + {{\sin }^2}A}&{\sin B + {{\sin }^2}B}&{\sin C + {{\sin }^2}C} \end{array}} \right| = 0$,then the triangle is

$\begin{vmatrix} \cos^2\theta & -\sin^2\theta \\ \sin^2\theta & \cos^2\theta \end{vmatrix} = \dots$

Prove that the determinant $\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|$ is independent of $\theta$.

If $A_{\lambda} = \begin{bmatrix} \lambda & \lambda - 1 \\ \lambda - 1 & \lambda \end{bmatrix}; \lambda \in N$,then $|A_1| + |A_2| + \dots + |A_{300}|$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module