# Matrices & Determinants Questions and Answers

Algebra
Matrices & Determinants
7 4 1 2 equation Ax x Let matrix A and vector x 4 find the constant value that satisfy the
Algebra
Matrices & Determinants
Find the general solution of the simple homogeneous system below which consists of a single linear equation Give your answer as linear combination of vectors Let x and x3 be free variables 2x 6x 8x3 0 O A O C X1 X X 4 X2 EHEHE X2 3 X X3 X3 X3 with X2 X3 free X X2 X 0 X3 with X2 X3 free X3 O B O D X BHOHE X2 X2 X3 with X2 X3 free 5 X2 BHOHO X x3 with X2 X3 free 4 0
Algebra
Matrices & Determinants
1 Consider the 6 x 6 matrix A 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 a 2 marks Compute A Hint Partition A as a block matrix to save yourself a lot work b 1 mark What do you think A2023 equals You do not have to rigorously prove yo in corrent but hrinflu oulain who think it s t
Algebra
Matrices & Determinants
Order Naproxen Sodium 0 75 grams Available Naproxen Sodium 375 mg per tablet How many tablet s will the nurse administer
Algebra
Matrices & Determinants
b B Let G A E GL R A d for some a b E R Prove that G a forms a subgroup of GL2 R the group of 2 x 2 invertible matrices with real entries Can you identify this group as something familiar Let be a closed binary operation on a set S and suppose that is associative and there is an identity element e In this case e call S under a semigroup Thus a group is just a semigroup where each element has an inverse
Algebra
Matrices & Determinants
Let AX B be a system of 7 linear equations in 6 variables and C its augmented matrix If the rank of A is 4 and the rank of C is 5 then which of the following statements is true Select one Select one There are no such system The system has no solution The system has a unique solution The system hon infinit inconsistent custom
Algebra
Matrices & Determinants
1 a Find the matrix P that multiplies every vector r y 2 R to produce the vector 3x 2y z 5y 2 8r Also find P 1 b Find the matrix P that multiplies every vector r y R2 to produce 5x 4y 2x 3y 2x R
Algebra
Matrices & Determinants
Select the simplified form of the difference 6n 8n 3 3n 2 8n 2 3n 4 6n 3
Algebra
Matrices & Determinants
Question 7 What is the result of the following matrix 2 5 6 2 5 3 2 3 1 3 1 5 1 2
Algebra
Matrices & Determinants
Express the following invertible matrix A as a product of elementary matrices You can resize a matrix when appropriate by clicking and dragging the bottom right corner of the matrix A 01 20 Number of Matrices 1 000
Algebra
Matrices & Determinants
e 3 Marks With the given enciphering matrix 13 Find the ciphertext for
Algebra
Matrices & Determinants
9 8 points Considering the following matrix A which are the singular values of A a 1 b 2 c 3 d 4 e 9 0 1 0 0 0020 0003 0000
Algebra
Matrices & Determinants
Given 2 x 3 matrix M find a 3 x 2 matrix B such that MB I where I is the 2 x 2 identity matrix 1 00 2 00 3 00 2 00 2 00 4 00 B 1 2 2 2 M X 0
Algebra
Matrices & Determinants
2 6 The vectors 1 5 0 1 21 2 02 1 2 1 4 relative to the 1 6 lattice basis Determine the coordinates of this site x 1 2 x3 relative to the standard basis of R 3 03 the crystal lattice of titanium One of the octahedral sites is Select Select 0 3 0 Select 2 0 A 0 in R form a basis for the unit cell of 4 8
Algebra
Matrices & Determinants
a 325 cm 622 cm 409 cm Triangular Right Prism with Right Triangular Bases b 15 ft 45 ft 22 ft 12 ft Trapezoidal Right Prism
Algebra
Matrices & Determinants
Determine the values of a for which the system has no solution excatly one solution or infinitely many solutions x 2y 3z 4 3x y 5z 2 4x y 7z a 2