If vmatrix -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 vmatrix = 4x, then x = Option 1: abc Option 2: a^2 b^2 c^2 Option 3: a + b + c Option 4: 0

Answer: a^2 b^2 c^2. Solution: Factor a, b, c from columns 1, 2, 3 of the determinant, then a, b, c from rows 1, 2, 3 to get a^2 b^2 c^2 vmatrix -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 vmatrix. Expanding the simple determinant gives 4. So determinant = 4 a^2 b^2 c^2 = 4x, giving x = a^2 b^2 c^2.

Applied Mathematics

Algebra

Medium

If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x$ , then $x =$

abc

$a^2 b^2 c^2$

$a + b + c$

✅ Correct Option: 2

Factor a, b, c from columns 1, 2, 3 of the determinant, then a, b, c from rows 1, 2, 3 to get $a^2 b^2 c^2 \begin{vmatrix} -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{vmatrix}$ . Expanding the simple determinant gives 4. So determinant $= 4 a^2 b^2 c^2 = 4x$ , giving $x = a^2 b^2 c^2$ .

2023: 30 May Shift 3

If the matrix $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfies the equation $A^T A = I_3$ , then $x^2 + y^2 + z^2$ is :

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. A matrix that has unequal number of rows and columns is called	I. Non-singular matrix
B. A matrix whose determinant is non-zero is called	II. Null matrix
C. A diagonal matrix whose diagonal elements are equal is called	III. Rectangular matrix
D. A matrix that is both symmetric and skew-symmetric is	IV. Scalar matrix

Choose the correct answer from the options given below:

2023: 22 May Shift 3

If the matrix $\begin{bmatrix} 0 & 2 & 5x \\ -2 & 0 & 6 \\ 10 & -6 & y \end{bmatrix}$ is skew-symmetric matrix, then the value of $(y - 4x)$ is :

2026: 14 May Shift 2

A and B are square matrices of order 3 each such that $|A|=3, |B|=2$ , then the value of $|4AB|$ will be?

2023: 11 Aug Shift 1

If $\begin{bmatrix} 2x & -7 \\ 5y & 8 \end{bmatrix} = \begin{bmatrix} 6 & -7 \\ -5 & 3x + y \end{bmatrix}$ , then value of $5x - 3y$ is :

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	A matrix which is both symmetric and skew symmetric	I.	symmetric matrix
B.	All positive integral powers of a symmetric matrix	II.	unit matrix
C.	Positive odd integral powers of a skew-symmetric matrix	III.	null matrix
D.	A square matrix $A = [a_{ij}]_{n\times n}$ with $a_{ij} = \begin{cases}0, & \forall\, i \neq j \\ 1, & \forall\, i = j\end{cases}$	IV.	skew-symmetric matrix

Choose the correct answer from the options given below:

If ∣−a2abacba−b2bcacbc−c2∣=4x\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x​−a2baac​ab−b2bc​acbc−c2​​=4x, then x=x =x=

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x$ , then $x =$