MATHS-3/10- MATRICES : MATHS-3/10- MATRICES BY
MANJULA B
manjulab64@gmail.com
KIND ATTENTION PLEASE : KIND ATTENTION PLEASE THIS SESSION RUNS FOR 60 MINUTES
PLEASE ENSURE YOUR SOUND SETTINGS
THIS IS AN AUDIO CLASS ONLY
ANY TECHNICAL PROBLEMS LIKE AUDIO DISTURBANCES, POWER CUTS AND INTERNET PROBLEMS ARE BEYOND MY CONTROL. I WILL TRY TO RESCHEDULE WHERVER NECESSARY
LAST TEN MINUTES DEVOTED FOR YOUR DOUBTS FOR CLARIFICATION
MORE DETAILS : email anytime manjula64@gmail.com
MATRICES : MATRICES A matrix is a rectangular arrangement of numbers in rows and columns enclosed within brackets
A matrix having only one row is called a row matrix and only one column is called column matrix.
The transpose of a matrix A is a matrix obtained by interchanging rows and columns of A and is represented by A’ and hence the transpose of a row matrix is a column matrix and viceversa
A matrix in which no. of rows is equal to no. of columns is called square matrix
MATRICES : MATRICES A square matrix in which all the elements except those on the principal diagonal are zero is a diagonal matrix
A diagonal matrix in which all the principal diagonal elements are the same is called scalar matrix and if all the diagonal elements are 1 is called unit matrix or identity matrix (dented by 1)
A matrix in which all the elements are zero is called null matrix or a zero matrix and represented by zero
TYPES OF MATRIX-CONTD : TYPES OF MATRIX-CONTD A matrix is said to be symmetric if A = A’
A matrix is said to be skew symmetric if A’ =- A.
The principal diagonal elements of a skew symmetric matrix are all zero
A matrix is multiplied by a scalar, each element of the matrix is multiplied by the scalar.
TYPES OF MATRIX-CONTD : TYPES OF MATRIX-CONTD When a matrix is multiplied by a scalar, the order does not change
Two matrices A and B can be added only if they are of the same order
If A is a square matrix, then A + A’ is symmetric and A-A’ is a skew symmetric
Addition of matrices is commutative ie., A+B = B+A AND Associative i.e., (A+B)+ C = A+ (B+C)
TYPES OF MATRIX -CONTD : TYPES OF MATRIX -CONTD If A and B are two matrices, the product AxB is possible if the number of columns in A is equal to the number of rows in B
If is mxn matrix and B is nxp matrix AB is possible because the no. of columns in A and no. of rows in B is n and the order of AB is mxp
The multiplication of matrices is carried out by adding the product of corresponding rows and columns of the matricesIf two matrices are equal, then corresponding elements will be equal.
TYPES OF MATRIX-CONTD : TYPES OF MATRIX-CONTD Matrix multiplication is not commutative and subtraction of matrices is also not commutative.
(A) = A
(AB ) = BA
AB IS NOT EQUAL BA except when B is the inverse of A.
SUMS SOLVED ON MATRIX : SUMS SOLVED ON MATRIX 1) If A = 4 -1 then show A-A’ is a skew symmetric matrix
3 -2
SUMS SOLVED ON MATRIX : SUMS SOLVED ON MATRIX 2) If A = 3 1 find A2(a Squared)
2 -4
Sums solved on matrix : Sums solved on matrix 3) If a = 3 1 Show that A2 – 8A + 131 = 0
2 5
Sums solved on matrix : Sums solved on matrix 4) If A = 4 -1 0 and B = -2 1 3,find x if A+x=B
2 3 1 4 5 -2
Sums on matrices : Sums on matrices 5)If A = -4 2 find A2 -2A +31
-3 3
Sums on matrices : Sums on matrices 6)Find x and y, given the following matrix
(3 -1) X = 15
2 5 Y -7
Sums on matrices : Sums on matrices 7) The order of matrix A is 2x3, find the order of its transpose
Sums on matrices : Sums on matrices 8) 2A = 4 -2 and 3B = 0 9, find A and B
-4 6 -3 3
Sums on matrices : Sums on matrices 9) Order of A is 2 x 2 , order of B is 3 x 2 and order of C is 2 x 3, which of the following matrix does not exist
AB’ BC BA CA
Sums on matrix : Sums on matrix 10) Given that A = 3 0, B = x y and that
0 4 0 z
And that AB A + B, find the value of x, y and z
CONCLUSION : CONCLUSION All the ten problems given are solved during the online class.
In case of any doubts or clarification noticed by a student subsequently, he is welcome to contact me through email any time for assistance
Students are welcome to bring to my notice any specific problem which could not be tackled in any subsequent class for solving depending upon the time availability. Other wise solution will be explained to the student in detail by e -mail.
Students are advised to feel free if they are not able to assimilate any topic to their satisfaction by bringing to me notice.
HAPPPY LEARNING
manjulab64@gmail.com
ATTENTION PLEASE : ATTENTION PLEASE THIS TUTORIAL IS UPLOADED IN WIZIQ SITE FOR A NOMINAL SUM
STUDENTS ARE ADVISED TO GO THROUGH THE PROBLEMS, WHERE SOLUTIONS ARE NOT GIVEN AND SEND THE SOLUTIONS TO ME FOR EVALUATION IF NECESSARY
SUGGESTIONS ARE ALWAYS SOUGHT FOR IMPROVEMENT
THANKS AGAIN, manjulab64@gmail.com
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