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Visual Solutions

8 step-by-step animated solutions for Matrices & Determinants. Each solution breaks the problem into visual clips with key insights.

PYQ 2024 · Jan 27 Shift 2Easy4 steps
Let AA be a 2×22 \times 2 real matrix and II be the identity matrix of order 2. If the roots of the equation ∣A−xI∣=0|A - xI| = 0 are −1-1 and 33, then the sum of the diagonal elements of the matrix A2A^2 is:
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PYQ 2024 · Jan 27 Shift 1Easy4 steps
Consider the matrix f(x)=[cos⁡x−sin⁡x0sin⁡xcos⁡x0001]f(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}.\n\nStatement I: f(−x)f(-x) is the inverse of f(x)f(x).\nStatement II: f(x)⋅f(y)=f(x+y)f(x) \cdot f(y) = f(x + y).\n\nWhich of the following is correct?
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PYQ 2024 · Jan (1 Feb) Shift 1Standard4 steps
If A=[21−12]A = \begin{bmatrix} \sqrt{2} & 1 \\ -1 & \sqrt{2} \end{bmatrix}, B=[1011]B = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}, C=ABATC = ABA^T and X=ATC2AX = A^TC^2A, then det⁡X\det X is equal to:
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PYQ 2024 · Jan (1 Feb) Shift 2Standard4 steps
Let the system of equations x+2y+3z=5x + 2y + 3z = 5, 2x+3y+z=92x + 3y + z = 9, 4x+3y+λz=μ4x + 3y + \lambda z = \mu have infinite number of solutions. Then λ+2μ\lambda + 2\mu is equal to:
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PYQ 2024 · Jan 29 Shift 1Standard4 steps
Let A=[1000αβ0βα]A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix} and ∣2A∣3=221|2A|^3 = 2^{21} where α,β∈Z\alpha, \beta \in \mathbb{Z}. Then a value of α\alpha is:
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PYQ 2024 · Apr 8 Shift 2Standard4 steps
If α≠a,β≠b,γ≠c\alpha \neq a, \beta \neq b, \gamma \neq c and ∣αbcaβcabγ∣=0\begin{vmatrix} \alpha & b & c \\ a & \beta & c \\ a & b & \gamma \end{vmatrix} = 0, then aα−a+bβ−b+γγ−c\frac{a}{\alpha - a} + \frac{b}{\beta - b} + \frac{\gamma}{\gamma - c} is equal to:
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PYQ 2024 · Apr 4 Shift 2Standard4 steps
Let A=[1201]A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} and B=I+adj(A)+(adj A)2+…+(adj A)10B = I + \text{adj}(A) + (\text{adj}\,A)^2 + \ldots + (\text{adj}\,A)^{10}. Then the sum of all elements of the matrix BB is:
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PYQ 2024 · Jan 31 Shift 1Tricky4 steps
If the system of linear equations\nx−2y+z=−4x - 2y + z = -4\n2x+αy+3z=52x + \alpha y + 3z = 5\n3x−y+βz=33x - y + \beta z = 3\nhas infinitely many solutions, then 12α+13β12\alpha + 13\beta is equal to:
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