Maths Midterm Exam Questions And Correct Verified Answers New Updated Version 2026
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Consider a 6 x 3 matrix A, a vector x of dimension 4, and a matrix B such that A ⋅ B ⋅ xis well-defined. What is the dimension of the
matrix B?
A B is a 3x4 matrix
B B is a 4 x 3 matrix
C B is a 3 x 3 matrix
D B is a 4 x 6 matrix
E B is a 6 x 4 matrix
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AT is a 3 x 6 matrix. Rest follows from the rules of matrix multiplication and the matrix-vector product.
Page 1/11 - Midterm05 - 152412.1.8
, Consider the system of linear equations
3y-6z=9
-2x+2y-6z=-12
3x-y+9y=44
This system has a unique solution. What is the value of y in this solution?
Feedback at question level
The augmented coefficient matrix is
By Gaussian elimination, the augmented coefficient matrix can be reduced to
1 0 0
[0 1 0]
0 1 0
0 0 1
Here, we first exchange the first two rows. Hence, the unique solution isx=4,y=13andz=5.
Page 2/11 - Midterm05 - 152412.1.8
T
Consider a 6 x 3 matrix A, a vector x of dimension 4, and a matrix B such that A ⋅ B ⋅ xis well-defined. What is the dimension of the
matrix B?
A B is a 3x4 matrix
B B is a 4 x 3 matrix
C B is a 3 x 3 matrix
D B is a 4 x 6 matrix
E B is a 6 x 4 matrix
Feedback at question level
AT is a 3 x 6 matrix. Rest follows from the rules of matrix multiplication and the matrix-vector product.
Page 1/11 - Midterm05 - 152412.1.8
, Consider the system of linear equations
3y-6z=9
-2x+2y-6z=-12
3x-y+9y=44
This system has a unique solution. What is the value of y in this solution?
Feedback at question level
The augmented coefficient matrix is
By Gaussian elimination, the augmented coefficient matrix can be reduced to
1 0 0
[0 1 0]
0 1 0
0 0 1
Here, we first exchange the first two rows. Hence, the unique solution isx=4,y=13andz=5.
Page 2/11 - Midterm05 - 152412.1.8
