SAMPLE PAPER-USAT-COMPUTER SCIENCEMATHEMATICS21. The sum of the series 2 + 2/3 + 2/9 + … is _____.A. 2B. 3C. 3.4D. 3.522. What is the rank of the matrix1 2 32 4 65 10 15
Question
SAMPLE PAPER-USAT-COMPUTER SCIENCEMATHEMATICS21. The sum of the series 2 + 2/3 + 2/9 + … is _____.A. 2B. 3C. 3.4D. 3.522. What is the rank of the matrix1 2 32 4 65 10 15
Solution
- The given series is a geometric series where the first term (a) is 2 and the common ratio (r) is 1/3. The sum of an infinite geometric series can be found using the formula S = a / (1 - r).
Substituting the given values, we get S = 2 / (1 - 1/3) = 2 / (2/3) = 3. So, the sum of the series is 3. Therefore, the answer is B. 3.
- The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. In the given matrix, the third row is a linear combination of the first two rows (5*1st row = 3rd row). Therefore, the rows are not linearly independent. Hence, the rank of the matrix is 2.
Similar Questions
The sum of the series 2 + 2/3 + 2/9 + … is _____.A. 2B. 3C. 3.4D. 3.522. What is the rank of the matrix1 2 32 4 65 10 15 ?A. 1B. 2C. 3D. 023. Solution of the equation sin2x = 1 is ______.A. ∏/4, 3∏/4B. 3∏/4, ∏/2C. ∏/4, 3∏/2D. 3∏/2, ∏/2ANSWER KEY1 D 7 C 13 A 19 D2 D 8 A 14 D 20 C3 D 9 D 15 B 21 B4 A 10 A 16 B 22 A5 D 11 C 17 A 23 D6 A 12 C 18 A
What is the rank of the matrix ⎡⎣⎢⎢⎢442670003639021328412⎤⎦⎥⎥⎥[473024062820314609312]?a.3b.4c.5d.2
Matrix A and B are given below:A =1 −3 4 −1 9−2 6 −6 −1 −10−3 9 −6 −6 −33 −9 4 9 0 and B =1 −3 0 5 −70 0 2 −3 80 0 0 0 50 0 0 0 0Assume that the matrix A is row equivalent to B. Find(a) (3 pts) rank A.
. Find the rank of the matrix A by normal form method where1 2 1 34 1 2 1 .3 1 1 21 2 0 1
The rank of the following matrix [123246369]⎣⎡ 123 246 369 ⎦⎤ is
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