Let \(u=\begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix}\), and let σ1, σ2, σ3, σ4, σ5 be the singular values of the matrix M= uuT (where uT is the transpose of u).The value of \(Σ^{5}_{i=1}σ_i\) is
Correct Answer: 55
Solution and Explanation
Top Questions on Matrix
Let $ A = \begin{bmatrix} 2 & 2 + p & 2 + p + q \\4 & 6 + 2p & 8 + 3p + 2q \\6 & 12 + 3p & 20 + 6p + 3q \end{bmatrix} $ If $ \text{det}(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n, \, m, n \in \mathbb{N}, $ then $ m + n $ is equal to:
Consider the balanced transportation problem with three sources \( S_1, S_2, S_3 \), and four destinations \( D_1, D_2, D_3, D_4 \), for minimizing the total transportation cost whose cost matrix is as follows:
where \( \alpha, \lambda>0 \). If the associated cost to the starting basic feasible solution obtained by using the North-West corner rule is 290, then which of the following is/are correct?
- Let \( p_A(x) \) denote the characteristic polynomial of a square matrix \( A \). Then, for which of the following invertible matrices \( M \), the polynomial \( p_M(x) - p_{M^{-1}}(x) \) is constant?
Then, which one of the following is TRUE?- Let \( A \) be a square matrix of order 3 such that \( \text{det}(A) = -2 \) and \( \text{det}(3 \cdot \text{adj}(-6 \cdot \text{adj}(3A))) = 2^{m+n} \cdot 3^{mn} \), where \( m > n \). Then \( 4m + 2n \) is equal to:
Questions Asked in GATE AR exam
- Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of 25 km/h and car Q travels East with a speed of 30 km/h. Car P travels continuously but car Q stops for some time after traveling for one hour. If both cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?
- GATE AR - 2025
- Direction sense
- A 24 cm line AB is vertically standing on a horizontal plane. The station point is located 18 cm above ground and 15 cm in front of the line AB. The picture plane is located in between the line AB and station point perpendicular to the sight line. The distance between the picture plane and the station point is 9 cm. The height of the perspective view of the line AB is ________cm. (rounded off to one decimal place)
- GATE AR - 2025
- Height & Distance
A four-arm uncontrolled un-signaled urban intersection of both-way traffic is illustrated in the figure. Vehicles approaching the intersection from the directions A, B, C, and D can move to either left, right, or continue in straight direction. No U-turn is allowed. In the given situation, the maximum number of vehicular crossing conflict points for this intersection is _________ (answer in integer)
- GATE AR - 2025
- Traffic survey methods, Traffic flow Analysis
An individual chooses a transport mode for a particular trip based on three attributes i.e., cost of journey (X), In-vehicle travel time to reach destination (Y), and Out-of-vehicle time taken to access mode at respective stops (Z). The values for these attributes for three modes Rail, Bus and Para-transit are given in the table. If the general utility (U) equation is \( U = - 0.5 \times X - 0.3 \times Y - 0.4 \times Z \), using the Logit model, the estimated probability of choosing Bus is _________ (rounded off to two decimal places).
- GATE AR - 2025
- Transportation
- The spot speeds (in km/h) of eight vehicles in a traffic stream are 42, 52, 56, X, 53, 62, 65, and 48. X is the spot speed of the fourth vehicle. The Time Mean Speed of the traffic stream is 56.25 km/h. After determining the value of X, the calculated Space Mean Speed of the traffic stream is _________ km/h. (rounded off to two decimal places)
- GATE AR - 2025
- Traffic survey methods, Traffic flow Analysis