1 A ……... is a rectangular array of numbers that are enclosed within a bracket .
horizontal
set
vertical
matrix
2 When the numbers of rows is equal to the numbers of columns equal to 'n'. Where m=n. Then is called…..
a square matrix
a column
a row
a matrix
3 What is this matrix called :
[0000]
diagonal matrix
proper matrix
zero matrix
square matrix
4 What is another name given to an identity matrix
unit matrix
diagonal matrix
special matrix
triangular matrix
5 Let A be a
n×n
square matrix . A is a symmetric matrix if A equal to …….
AT
B
C
4BT
6 Commpute the matrix :
∣∣∣102−5−314−1∣∣∣+∣∣∣32−506−2−1−3∣∣∣
∣∣∣42−3−73−13−4∣∣∣
∣∣∣42−3−53−13−4∣∣∣
∣∣∣41−3−53−13−4∣∣∣
∣∣∣423−53−13−4∣∣∣
7 Let A=
∣∣∣2003∣∣∣
and B=
∣∣∣70011∣∣∣
. Find AB
∣∣∣140033∣∣∣
∣∣∣14003∣∣∣
∣∣∣10033∣∣∣
∣∣∣40033∣∣∣
8 Solve the linear equation : 2x+y-3z= 5,3 x-2y-2z= 5, and 5x-3y-z= 16.
(1 , 3 , -2 )
(1 , -3 , 2 )
(1 , -3 , -1 )
(1 , -3 , -2 )
9 Two systems of linear equations involving the same variables are said to be ......, if they have the same solution set.
matrix
subset
equivalent
commutative
10 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for a
2
4
7
3
even if you don't know #1, it's evident from the other questions that this is an exercise set involving matrices.
#10: a=2
Now, what ideas do you have on the others?
1. A matrix is a rectangular array of numbers that are enclosed within a bracket. The numbers can be arranged in horizontal rows and vertical columns.
2. When the number of rows is equal to the number of columns in a matrix, it is called a square matrix. In a square matrix, the number of rows (m) is equal to the number of columns (n), so m = n.
3. The matrix [0000] is called a zero matrix. It is a diagonal matrix where all the elements outside the main diagonal are zero.
4. Another name given to an identity matrix is a unit matrix. It is a special type of square matrix where all the elements on the main diagonal are ones, and all the elements outside the main diagonal are zeroes.
5. A square matrix A is considered symmetric if it is equal to its transpose. In other words, A = A^T, where A^T is the transpose of matrix A.
6. To compute the given matrix:
∣∣∣102−5−314−1∣∣∣+∣∣∣32−506−2−1−3∣∣∣
∣∣∣42−3−73−13−4∣∣∣
∣∣∣42−3−53−13−4∣∣∣
∣∣∣41−3−53−13−4∣∣∣
∣∣∣423−53−13−4∣∣∣
You need to perform matrix addition between the corresponding elements of the two matrices given within the brackets. The resulting matrix will be:
∣∣∣2-8-1-9∣∣∣
∣∣∣6-2-2-4∣∣∣
∣∣∣6-2-1-4∣∣∣
∣∣∣5-2-1-4∣∣∣
7. To find AB for the given matrices:
A = ∣∣∣2003∣∣∣ and B = ∣∣∣70011∣∣∣
You need to perform matrix multiplication between matrix A and matrix B. The resulting matrix will be:
AB = ∣∣∣140033∣∣∣
8. To solve the linear equation:
2x + y - 3z = 5,
3x - 2y - 2z = 5,
5x - 3y - z = 16.
You can use various methods such as substitution, elimination, or matrix methods to find the solution. The solution for this equation is (1, -3, -2).
9. Two systems of linear equations involving the same variables are said to be equivalent if they have the same solution set. It means that the two systems produce the same answer for all possible values of the variables.
10. To solve the set of linear equations using the matrix method:
a + 3b + 2c = 3,
2a - b - 3c = -8,
5a + 2b + c = 9.
You can represent the system of equations in matrix form as AX = B, where A is the coefficient matrix of the variables, X is the vector of variables, and B is the constant matrix.
By solving the matrix equation AX = B, you can find the values of the variables. In this case, solving the matrix equation will give the value of a as 2.